investing in educational excellence (ie · lo(3.a.3.1): the student is able to analyze a scenario...

Updated Version March 2015 Submit to Area Assistant Superintendent

School ___________________________________ Principal _______________________________

Date _____________________________________ Desired Implementation Date ______________

Part 1: Complete in preparation for consultation with Area Assistant Superintendent.

Describe your idea:

Specifically, we want to combine the Advanced Placement Physics I course with the Advanced

Placement Physics C - Mechanics course for our Math and Science Academy as well as our Engineering

Academy students during their junior year. The AP Physics I curriculum encompasses all but ten of the

learning objectives of the AP Physics C Mechanics course, and those ten Learning Objectives have to do

with the use of calculus to more rigorously investigate the physics concepts involved.

End Result:

These Math and Science Academy students will graduate with at least 5 Advanced Placement Science

courses on their transcript and most will opt for another one or two during their senior year. The

increased rigor and opportunity to graduate with between 5 and 7 AP college credits is one of the

factors that makes the Academies of Pope a more lucrative and enticing choice for our students when

they consider choosing one of the magnet programs offered within the county. Additionally, the

number of possible credits is also a factor that makes the Academies of Pope comparable to the

possibilities that exist in the Block Scheduled schools in the county.

Rationale:

These Math and Science Academy students will already have completed a year of AP Calculus AB and

will be taking AP Calculus BC so the incorporation of the calculus will utilize the mathematics skills they

have already mastered. This combination course will allow the students to gain a full and complete

understanding both conceptually from the Physics I course and mathematically from the Physics C

course.

Investing in Educational Excellence (IE2) Idea to Implementation Form

Alan C. Pope HS Robert Downs

11/9/15 Fall 2016


What data has prompted / guided this idea:

A) Student interviews

Having discussed the Physics C Mechanics course and the AP Physics course differences and

expectations with my former Physics I students now taking Mechanics C, there is a consensus that had

they known the calculus, it would have been not only been easier to learn in in the Physics I course, but

would have improved the course and given them a more complete feeling of mastery, where they now

feel like the lion’s share of Mechanics C is review with the tidbits of calculus scattered throughout when

required.

One of the reasons we started the Math and Science Academy at Pope was to offer the students

in our attendance a viable, attractive, and competitive option to the magnet programs that exist within

the county. The Math and Science Academy students are automatically scheduled to take four AP

science courses; Environmental, Biology, Chemistry and Physics I. This pairing will automatically give

them a fifth AP science credit on their transcript and a fifth opportunity to earn college credit or

advanced standing. Most of the students in the Math and Science Academy will probably take a sixth

AP Science and we expect several to take a seventh, which would rival or beat any of the magnet or

block schedule schools in the area, which was the impetus behind the creation of the Academies at

Pope.

B) Having taught both the AP Physics I and AP Physics C mechanics courses, I know the time

requirements which must be followed to complete each course, and the incorporation of the

calculus in those few objectives where it is mentioned will not significantly impact the conduct

of the course. The additional inquiry and laboratory experiences will give these students a more

in depth and thorough treatment of Mechanics without having to expend two of their 24 credits

to do so.

C) Working with the kids at Pope who would have been the Math and Science Academy had it

existed, and having surveyed them, I am confident that this segment of our population will

thrive under the combination of the AP Physics courses. The AP Physics I course is designed to

be a yearlong course to allow extra time for the laboratory component, and the Mechanics C

course has been taught here in that some format; a year to cover what is basically one semester

of college level material. This will allow more than adequate time to imbed the calculus learning

objectives into the AP Physics I curriculum.

D) The grading for this course will be such that students will receive ½ Credit for AP Physics I and ½

credit for AP Physics C Mechanics each semester for a total of two credits at the completion of

the year. With the overlap of the majority of the learning objectives, the combination of the

courses warrants the double credit opportunity.


Describe how you will monitor and measure the effectiveness of the implementation:

A) In class assessment and monitoring – I track the grades of AP Physics Students from year to year

and compare them to make sure they are relatively consistent. I will also be able to compare

the grades of the Academy students with those of the regular AP Physics I students and see if

they are still on par for the course as well as predicting their success on the AP Exams. I have a

limited comparative numbers for the Physics C students I have taught in the past as well.

B) The most telling measure will be the AP exam scores, and the use of the instructional planning

report produced by the College Board for each exam.

C) Communication and feedback from students during in-class discussion regarding their comfort

with material, pace of the course, and academic/college/career goals.

D) Communication and feedback from students and parents

Part 2: Complete after consultation with Area Assistant Superintendent in preparation for Impact

Evaluation Team and Executive Cabinet review and validation.

Describe Budget Implications:

None

Describe Timeline for Communication and Implementation:

Meet with parents and students upon approval, then maintain updates on my blog, along with

semiannual Open House dates.


For Impact Evaluation Team Use Only:

Academics Accountability

& Research Financial Services

Human Resources

Chief of Staff

Leadership & Learning

Operations Technology


AP Physics I and AP Physics C

Learning Objectives Compared

Learning Objectives

AP Physics C - Mechanics AP Physics I A.1a and b – Students should understand relationships among position, velocity, and acceleration. Given expression of x v or a, determine the other two as functions of time Produce and interpret graphs of motion Use kinematics equations to solve problems Sketch graphs of motion

Learning Objective (3.A.1.1): The student is able to express the motion of an object using narrative, mathematical, and graphical, representations. [See Science Practices 1.5, 2.1, and 2.2] Learning Objective (3.A.1.2): The student is able to design an experimental investigation of the motion of an object. [See Science Practice 4.2] Learning Objective (3.A.1.3): The student is able to analyze experimental data describing the motion of an object, and is able to express the results of the analysis using narrative, mathematical, and graphical, representations. [See Science Practice 5.1] LO (4.A.2.3): The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. [Sci Pr 1.4 and 2.2]

A.1 c – given velocity vs time function, write and solve the differential equation for v(t)

A.2 a Add, subtract, resolve displacement and velocity vectors. Determine components, net displacement and change in velocity A.2.b Understand general motion of particle in two dimensions so that given functions for x and y, they can determine components, magnitude and direction of velocity and acceleration A.2.c – understand motion of projectiles in uniform gravitational field. Sketch or identify graphs of position, and velocity as functions of time

3.E.1.c – Net force exerted on an object perpendicular to the direction of motion can change the direction without changing kinetic energy: including projectile and uniform circular motion LO (3.E.1.3): The student is able to use force and velocity vectors to determine qualitative or quantitatively the net force on an object and qualitatively whether kinetic energy of that object would increase, decrease, or remain unchanged. [Sci Pr 1.4 and 2.2] LO (3.E.1.4): The student is able to apply mathematical routines to determine the change in kinetic energy of an object given the forces on the object and the displacement of the object. [Sci Pr 2.2]


AP Physics C Mechanics AP Physics I

B.1 - students should be able to analyze situations where a particle or system remains at rest or constant velocity under the influence of several forces.

LO(3.A.3.1): The student is able to analyze a scenario and make claims (develop arguments, justify assertions) about the forces exerted on an object by other objects for different types of forces or components of forces. [See science practices 6.4 and 7.2] LO (3.b.1.2): The student is able to design a plan to collect and analyze data for motion (static, constant or accelerating) from force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces. [See science practices 4.2 and 5.1] LO (3.B.1.3): The student is able to re-express a free body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object. [See science practices 1.5 and 2.2]

B.2.a Students should understand relation between force acting on an object and the resulting change in velocity so: B.2.a.1 Calculate velocity change for constant force. B.2.a.2 Calculate velocity change when a force F(t) acts for specified time B.2.a.3 Determine average force involved in specified change in velocity over specified time

LO (3.b.1.2): The student is able to design a plan to collect and analyze data for motion (static, constant or accelerating) from force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces. [See science practices 4.2 and 5.1] LO (3.B.1.3): The student is able to re-express a free body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object. [See science practices 1.5 and 2.2]



B.2.b – Understand Newton’s 2nd law, F = ma as it applies to an object subject to gravity, tensions or contact forces B.2.b.1 Draw free body diagrams B.2.b.2 Write vector equations using forces and components using Newton’s 2nd law B.2.b – Understand Newton’s 2nd law, F = ma as it applies to an object subject to gravity, tensions or contact forces B.2.b.1 Draw free body diagrams B.2.b.2 Write vector equations using forces and components using Newton’s 2nd law B.2.c Analyze situations with specified acceleration to determine net force in situations with up and down motion and constant acceleration. B.2.d 1-3 understand normal and frictional forces. Objects moving on rough inclines and when an object will start to slip

LO (3.A.2.1): The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with magnitude, direction and units during the analysis of a situation. [See science practice 1.1] LO (3.B.1.1): The student is able to predict the motion of an object subject to forces exerted by several objects using and application of Newton’s second law in a variety of situations with acceleration in one dimension. [See science practices 6.4 and 7.2] LO (3.b.1.2): The student is able to design a plan to collect and analyze data for motion (static, constant or accelerating) from force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces. [See science practices 4.2 and 5.1] LO (3.B.1.3): The student is able to re-express a free body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object. [See science practices 1.5 and 2.2] LO (3.B.2.1): The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively. [See science practices 1.1, 1.4, and 2.2] LO (3.C.4.1): The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces. [See science practice 6.1] LO (3.C.4.2): The student is able to explain contact forces (tension, friction, normal, spring) as arising from interatomic electric forces and that they therefore have certain direction. {See Science Practice 6.2]

B.2.e.1-5 Effect of Drag forces on objects Writing and solving differential equation for an object’s velocity as a function of time. Derive an expression for acceleration of an object falling under influence of drag forces

Learning Objective (2.B.1.1): The student is able to apply Fw =mg to calculate the gravitational force on an object with mass m in a gravitational field of strength g in the context of the effects of a net force on objects and systems. [See Science Practices 2.2 and 7.2] Learning Objective (3.A.1.1): The student is able to express the motion of an object using narrative, mathematical, and graphical, representations. [See Science Practices 1.5, 2.1, and 2.2] LO (3.A.2.1): The student is able to represent forces in diagrams or mathematically using appropriately labeled


vectors with magnitude, direction and units during the analysis of a situation. [See science practice 1.1]


3.a-d Newton’s third law – Identify force pairs Analyze contact forces for objects moving simultaneously Tension is constant in light strings over massless pulleys Solve problems with Newton’s laws leading to two or three simultaneous linear equations involving unknown accelerations or forces.

Learning objective (3.A.4.1): The student is able to construct explanations of physical situations involving the interaction of bodies using Newton’s third law and the representation of action-reaction pairs of forces. [See science practices 1.4 and 6.2] Learning objective (3.a.4.2): The student is able to use Newton’s third law to make claims and predictions about the action-reaction pairs of forces when two objects interact. [See science practices 6.4 and 7.2] Learning objective (3.a.4.3): The student is able to analyze situations involving interactions among several objects by using free body diagrams that include the application of Newton’s third law to identify forces. [See science practice 1.4]

C. Work, Energy and Power C.1 – definition of work C.1.a.1-4 Calculate work by constant force Relate work to area under curve of F vs t graph Integrate to calculate work performed by a force, F(x) on object in one dimension Calculate work done by specified force during displacement in a plane C.1.b.1-3 Calculate change in kinetic energy or speed from a specified amount of work. Calculate the work when an object undergoes specified change in KE or speed. Calculate a change in kinetic energy or speed that result from the application of specified forces, or determine the force required to bring an object to rest in a specified distance. C.2.a – State definition of conservative force and describe examples of conservative and non-conservative forces C.2.b1-5 State relationship between forces and potential energy Calculate the potential energy function associated with a one-dimensional force F(x)

LO (3.E.1.1): The student is able to make predictions about the changes in kinetic energy of an object based on the consideration of the direction of the net force on the object as the object moves. [Sci Pr 6.4 and 7.2] LO (3.E.1.2): The student is able to use net force and velocity vectors to determine qualitatively whether kinetic energy of an object would increase, decrease or remain unchanged. [Sci Pr 1.4] LO (3.E.1.3): The student is able to use force and velocity vectors to determine qualitative or quantitatively the net force on an object and qualitatively whether kinetic energy of that object would increase, decrease, or remain unchanged. [Sci Pr 1.4 and 2.2] LO (4.A.3.2): The student is able to use the visual or mathematical representations of the forces between objects in a system to predict whether or not there will be a change in the center-of-mass velocity of that system. [Sci Pr 1.4] Lo (4.B.2.2): The student is able to perform analysis on data presented as a force-time graph and predict the change in momentum of a system. [Sci Pr 5.1] LO (4.C.1.2): The student is able to predict changes in the total energy of a system due to changes in position


Calculate the magnitude and direction of a one-dimensional force when given the Potential energy function U(x) Write an expression for the force exerted by an ideal spring and for the potential energy for a stretched or compressed spring. Calculate the potential energy for one or more objects in a uniform gravitational field.

and speed of objects or frictional interactions within the system. [Sci Pr 6.4] LO (4.C.2.1): The student is able to make predictions about the changes in mechanical energy of a system when a component of an external force acts parallel or anti


C.3.a 1-3 understand mechanical and total energy State relationship between work performed and change in mechanical energy Describe and identify situations where mechanical energy is converted to other forms of energy Analyze situations in which mechanical energy is changed by friction or another outside force. C.3.b 1-4 Identify situations where mechanical is or is not conserved. Apply conservation of energy in analyzing: Systems like the Atwood machine, Systems with springs Objects under the influence of other non- constant one-dimensional forces/ C.3.c solve problems involving both Newton’s laws and energy conservation. C.4.a and b Students should calculate power required to maintain the motion of an object with constant acceleration. Calculate the work done by a force that supplies constant power or the average power supplied by a force to do a specified amount of work.

-parallel to the direction of the displacement of the center of mass. [Sci Pr 6.4] LO (4.C.2.2): The student is able to apply the concepts of Conservation of Energy and the Work-Energy theorem to determine qualitatively and/or quantitatively that work done on a two object system in linear motion will change the kinetic energy of the center of mass of the system, and/or, the internal energy of the system. [Sci Pr 1.4, 2.2, 7.2] LO (5.B.1.1): The student is able to set up a representation or model showing that a single object can only have kinetic energy and use information about the object to calculate its kinetic energy. [Sci Pr 1.4 and 2.2] LO (5.B.1.2): The student is able to translate between a representation of a single object, which can only have kinetic energy, and a system that includes the object, which may have both potential and kinetic energy. [Sci Pr 1.5] LO (5.B.3.3): The student is able to apply mathematical reasoning to create a description of the internal potential energy of as system from a description of the objects and interactions in that system. [Sci Pr 1.4 and 2.2] LO (5.B.4.2): The student is able to calculate changes in kinetic energy and potential energy of a system, using information from representations of that system. [Sci Pr 1.4, 2.1, and 2.2] LO (5.B.5.1): The student is able to design an experiment and analyze data to examine how a force exerted on an object or system does work on the object or system as it moves through a distance. [Sci Pr 4.2 and 5.1] LO (5.B.5.2): The student is able to design an experiment to analyze graphical data in which interpretations of the area under a force distance curve are needed to determine the work done on or by an object or system. [Sci Pr 4.2 and 5.1] LO (5.B.5.3): The student is able to predict and calculate from graphical data the energy transfer to or work done on an object or system from information about a force exerted on the object or system through a distance. [Sci Pr 1.4, 2.2, and 6.4]


LO (5.B.5.4): The student is able to make claims about the interaction between a system and its environment in which the environment exerts a force on the system, thus doing work on the system and changing the energy of the system (kinetic plus potential energy). [Sci Pr 6.4 and 7.2] LO (5.B.5.5): The student is able to predict and calculate the energy transfer to (i.e. the work done on) an object or system from information about a force exerted on the object or system through a distance. [Sci 2.2 and 6.4]


D. 1-3 Systems of Particles D.1.a.1and 2 – Students should be able to identify by inspection the center of mass of a symmetrical object or Locate the center of mass of a system consisting of two such objects. D.1.a.3 Use integration to find the center of mass of a thin rod of non-uniform density D.1.b Students should understand the relation between center of mass velocity and linear momentum, and between center of mass and net external force for a system of particles. D.1.c Students should be able to define center of gravity and use this to express the gravitational potential energy in terms of center of gravity D.2.a-e Relate mass, velocity and linear momentum for an object and system of objects Relate impulse to the change in linear momentum and the average force acting on an object. State and apply relations between linear momentum and center of mass motion for a system of particles. Calculate area under force vs time curve and relate it to change in linear momentum Calculate the change in momentum of an object given a function F(t) for the net force acting on the object D.3.a1-5

LO (3.D.1.1): The student is able to justify the selection of data needed to determine the relationship between the direction of the force acting on an object and the change in momentum caused by that force. Learning Objective (3.D.2.1): The student is able to justify the selection of routines for the calculation of the relationships between changes in momentum of an object, average force, impulse, and time of interaction. Learning Objective (3.D.2.2): The student is able to predict the change in momentum of an object from the average force exerted on the object and the interval of time during which the force is exerted. Learning Objective (3.D.2.3): The student is able to analyze data to characterize the change in momentum of an object from the average force exerted on the object and the interval of time during which the force is exerted. LO (3.D.2.4): The student is able to design a plan for the collecting of data to investigate the relationship between changes in momentum and the average force exerted on an object over time. [Sci pr 4.2] LO (4.A.1.1): The student is able to use representation of the center of mass of an isolated two-object system to analyze the motion of the system qualitatively and semi-quantitatively. [Sci Pr 1.2, 1.4, 2.3,and 6.4] LO (4.A.2.1): The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time. [Sci Pr 6.4] LO (4.A.2.3): The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. [Sci Pr 1.4 and 2.2]


Explain how conservation of momentum follows as a consequence of Newton’s 3rd law Identify situations in which linear momentum or a component of linear momentum is conserved Apply conservation of linear momentum to one-dimensional elastic and inelastic collisions and two dimensional completely inelastic collisions Apply conservation of linear momentum two dimensional elastic and inelastic collisions. Analyze situations in which two or more objects are pushed apart by a spring or other agency, and calculate how much energy is released in the process D.3.b Understand frame of reference to analyze motion of an object relative to a moving medium, like a stream. Analyze the motion of particles relative to an accelerating frame of reference.

LO (4.A.3.1): The student is able to apply Newton’s second law to systems to calculate the change in the center-of-mass velocity when an external force is exerted on the system. [Sci Pr 2.2] LO (4.A.3.2): The student is able to use the visual or mathematical representations of the forces between objects in a system to predict whether or not there will be a change in the center-of-mass velocity of that system. [Sci Pr 1.4] LO (4.B.1.1): The student is able to calculate the change in linear momentum of a two object system with constant mass in linear motion from a representation of the system. (data, graphs, etc.) LO (4.B.1.2): The student is able to analyze data to find the change in linear momentum for a constant-mass-system using the product of the mass and the change in velocity of the center of mass. [Sci Pr 5.1] LO (4.B.2.1): The student is able to apply mathematical routines to calculate the change in momentum of a system by analyzing the average force exerted over a certain time on the system. [Sci Pr 2.2] LO (5.A.2.1): The student is able to define open and closed systems for everyday situations and apply conservation concepts for energy and linear momentum to those situations. [Sci Pr 6.4 and 7.2] LO (5.D.1.1): The student is able to make qualitative predictions about natural phenomena based on conservation of linear momentum and restoration of kinetic energy in elastic collisions. [Sci Pr 6.4 and 7.2] LO (5.D.1.2): The student is able to apply the principles of conservation of momentum and restoration of kinetic energy to reconcile a situation that appears to be isolated and elastic, but in which data indicate that linear momentum and kinetic energy are not the same after the interaction, by refining a scientific question to identify interactions that have not been considered. Students will be expected to solve qualitatively and/or quantitatively for one-dimensional situations and only qualitatively in two-dimensional situations.



E.1.a and b Uniform Circular motion – Relate radius of the circle and speed to radial acceleration Describe the direction of the particles acceleration and velocity at any time during the motion.

3.E.1.c – Net force exerted on an object perpendicular to the direction of motion can change the direction without changing kinetic energy: including projectile and uniform circular motion

E.1.c Determine components of velocity and acceleration at any instant and sketch or identify graphs of these quantities E.1.d – Analyze situations where an object moves in a horizontal or vertical circle to determine magnitude or direction of the net force or one of the components

Learning Objective (3.A.1.3): The student is able to analyze experimental data describing the motion of an object, and is able to express the results of the analysis using narrative, mathematical, and graphical, representations. [See Science Practice 5.1] LO (4.A.2.3): The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. [Sci Pr 1.4 and 2.2]

E.2.a Calculate magnitude and direction of torque due to a given force and calculate torque on a rigid object E.2.b Students should be able to state conditions for rotational and static equilibrium and analyze the equilibrium of a rigid object under the combined influence of a number of coplanar forces applied at different locations E.2.c develop qualitative understanding of rotational inertia so they can determine by inspection which set of symmetrical objects of equal mass has the greatest rotational inertia. E.2.d – Students should be able to calculate the rotational inertia of: a collection of point masses lying in a plane about an axis perpendicular to the plane, a thin rod of uniform density, a thin cylindrical shell about an axis or an object that may be viewed as being made up of coaxial shells Students should be able to state and apply the parallel axis theorem E.3.a Students should be able to write and apply relations among angular velocity, displacement and

LO (3.F.11): The student is able to use representations of the relationship between force and torque.[Sci Pr 1.4] LO (3.F.1.2): The student is able to compare the torques on an object caused by various forces. [Sci Pr 1.4] LO (3.F.1.3): The student is able to estimate the torque on an object caused by various forces in comparison to other situations. [Sci Pr 2.3] LO (3.F.1.4): The student is able to design an experiment and analyze data testing a question about torques in a balanced rigid system. [Sci Pr 4.1, 4.2, and 5.1] LO (3.F.1.5): The student is able to calculate torques on a two dimensional system in static equilibrium, by examining a representation or model (such as a diagram or physical construction) [Sci Pr 1.4 and 2.2] LO (5.E.1.1): The student is able to make qualitative predictions about the angular momentum of a system for


acceleration of an object that rotates about a fixed axis with constant angular acceleration. E.3.b Student should be able to use the right hand rule to associate an angular velocity vector with a rotating object E.3.c Describe the analogy between fixed axis rotation and straight line translation Determine angular acceleration when a rigid object is subjected to a specified external torque Determine radial and tangential acceleration Apply conservation of energy to problems of fixed axis rotation Analyze problems involving strings and massive pulleys E.3.d Students can justify and apply the relation between angular velocity and acceleration or between linear velocity and acceleration for a circular object that rolls without slipping along a fixed plane, and determine the velocity and acceleration of an arbitrary point on such an object. Apply the equations of translational and rotational motion simultaneously when analyzing slipping without rolling Calculate the total kinetic energy of an object that is undergoing both translational and rotational motion and apply energy conservation in such motion E.4.a Use right hand rule and vector cross product to calculate torque, angular momentum vector, for a moving particle and rigid object E.4.b Students should recognize conditions under which the law of conservation is applicable and relate this to one and two object systems like satellite orbits. State the relation between net external torque and angular momentum and identify situations in which angular momentum is conserved. Analyze problems in which moment of inertia of an object is changed when it rotates freely around a fixed axis. Analyze a collision between a moving particle and a rigid object that can rotate about a fixed axis or its center of mass

a situation in which there is no net external torque. [Sci Pr 6.4 and 7.2] LO (5.E.1.2): The student is able to make calculation of quantities related to the angular momentum of a system when the net external torque on a system is zero. [Sci Pr 2.1 and 2.2] LO (5.E.2.1): The student will be able to describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a fixed set of extended objects and point masses. [Sci Pr 2.2] LO (4.D.2.1): The student is able to describe a model of a rotational system and use that model to analyze a situation in which angular momentum changes due to interaction with other objects or systems. [Sci Pr 1.2 and 1.4] LO (4.D.2.2): The student is able to plan a data collection and analysis strategy to determine the change in angular momentum of a system and relate it to interactions with other objects and systems. [Sci Pr 4.2} LO (4.D.3.1): The student is able to use appropriate mathematical routines to calculate values for initial or final angular momentum, or change in angular momentum of a system, or average torque or time during which the torque is exerted in analyzing a situation involving torque and angular momentum. [Sci Pr 2.2] LO (4.D.3.2): The student is able to plan a data collection strategy designed to test the relationship between the change in angular momentum of a system and the product of the average torque applied to the system and the time the torque is exerted. [Sci 4.1 and 4.2] LO (5.E.2.1): The student will be able to describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a fixed set of extended objects and point masses. [Sci Pr 2.2] LO (4.D.2.1): The student is able to describe a model of a rotational system and use that model to analyze a situation in which angular momentum changes due to interaction with other objects or systems. [Sci Pr 1.2 and 1.4]



F. Oscillations and Gravitation – Students should be able to F.1a Sketch or identify a graph of displacement as a function of time, and determine amplitude, period and frequency of the motion F.1.b write down an appropriate expression A sin ωt or A cos ωt to describe the motion F.1.c – Find an expression for velocity as a function of time F.1.d –State the relations between acceleration, velocity and displacement and determine minimum or maximum values from the graph F.1.e – State the relation between frequency and period F.1.f- Recognize that a system that obeys the differential equation of the form d2x/dt2 = – ω2 x must execute simple harmonic motion F.1.g – State how the total energy of an oscillating system depends upon amplitude of the motion, sketch or identify a graph of potential or kinetic energy as function of time and identify mins and maxes. F.1.h Calculate kinetic and potential energies of an oscillating system as functions of time, sketch or identify graphs of these functions and prove that the sum of kinetic and potential energy is constant F.1.i- Calculate the max displacement of velocity of a particle that moves in simple harmonic motion with specified initial position and velocity. F.1.j - Develop a qualitative understanding of resonance so they can identify situations in which a system will resonate in response to a sinusoidal external force.

LO (3.B.3.1): The student is able to predict which properties determine the motion of a simple harmonic oscillator and what dependence of the motion is on those properties. [See science practices 6.4 and 7.2] LO(3.B.3.2): The student is able to design a plan and collect data in order to ascertain the characteristics of the motion of a system undergoing oscillatory motion caused by a restoring force. [See science practices 4.2] LO(3.B.3.3): The student can analyze data to identify qualitative or quantitative relationships between given values and variables (i.e., force, displacement, acceleration, velocity, period of motion, frequency, spring length, mass) associated with the objects in oscillatory motion to use that data to determine the value of an unknown. [See science practices 2.2 and 5.1] LO (3.B.3.4): The student is able to construct a qualitative and/or quantitative explanation of oscillatory behavior given evidence of a restoring force. [See science practices 2.2 and 6.2]


AP Physics C Mechanics AP Physics I F.2.a-e Mass on a spring Students can derive and apply the expression for the period of oscillation of a mass on a spring. Analyze problems where a mass is attached to a spring and oscillates horizontally or vertically. Determine the period of oscillation for systems involving series or parallel combinations of identical springs, or springs of different length. F.3.a-d Simple Pendulum Student should be able to derive and apply the expression for the period of a simple pendulum, State what approximation must be made in deriving the period of a simple pendulum, Analyze Motion of a torsional pendulum or physical pendulum in order to determine the period of small oscillations.

LO (3.B.3.1): The student is able to predict which properties determine the motion of a simple harmonic oscillator and what dependence of the motion is on those properties. [See science practices 6.4 and 7.2] LO(3.B.3.2): The student is able to design a plan and collect data in order to ascertain the characteristics of the motion of a system undergoing oscillatory motion caused by a restoring force. [See science practices 4.2] LO(3.B.3.3): The student can analyze data to identify qualitative or quantitative relationships between given values and variables (i.e., force, displacement, acceleration, velocity, period of motion, frequency, spring length, mass) associated with the objects in oscillatory motion to use that data to determine the value of an unknown. [See science practices 2.2 and 5.1] LO (3.B.3.4): The student is able to construct a qualitative and/or quantitative explanation of oscillatory behavior given evidence of a restoring force. [See science practices 2.2 and 6.2]

F.4.a-c Newton’s Law of Gravity Students should: Determine the force that one spherically symmetrical mass exerts on another Determine the strength of the gravitational field at a specified point outside the spherically symmetrical mass. Describe the gravitational force inside and outside a uniform sphere, and calculate how the field at the surface depends on the radius and density of the sphere

Learning Objective (2.B.1.1): The student is able to apply Fw =mg to calculate the gravitational force on an object with mass m in a gravitational field of strength g in the context of the effects of a net force on objects and systems. [See Science Practices 2.2 and 7.2] Learning Objective (2.B.2.1): The student is able to apply g = GM/r2 to calculate the gravitational field due to an object with mass m, where the field is a vector directed toward the center of the object of mass M. [See Science Practice 2.2] Learning Objective (2.B.2.2): The student is able to approximate a numerical value of the gravitational field


AP Physics C Mechanics

(g) near the surface of an object from its radius and mass relative to those of the Earth or other reference objects. [See Science Practice 2.2]

AP Physics I

F.5.a Circular orbits Students should recognize that motion does not depend upon mass and they should derive the expressions for velocity and period for circular orbits. Derive Kepler’s 3rd law for circular orbits and Derive and apply the relations among kinetic and potential energy for circular orbits F.5.b General orbits Students should State Kepler’s three Laws of planetary motion and use them to describe in qualitative terms the motion of an object in an elliptical orbit. Apply Energy and Angular momentum conservation to: Determine velocity and radial distance at any point in the elliptical orbit or relate the speeds of an object at the two extreme points in the elliptical orbit. Apply energy conservation in analyzing the motion of an object that is projected straight up from a planet’s surface or that is projected directly toward a the planet from far above the surface

LO (3.E.1.1): The student is able to make predictions about the changes in kinetic energy of an object based on the consideration of the direction of the net force on the object as the object moves. [Sci Pr 6.4 and 7.2] LO (3.E.1.2): The student is able to use net force and velocity vectors to determine qualitatively whether kinetic energy of an object would increase, decrease or remain unchanged. [Sci Pr 1.4] LO (3.E.1.3): The student is able to use force and velocity vectors to determine qualitative or quantitatively the net force on an object and qualitatively whether kinetic energy of that object would increase, decrease, or remain unchanged. [Sci Pr 1.4 and 2.2] LO (3.E.1.4): The student is able to apply mathematical routines to determine the change in kinetic energy of an object given the forces on the object and the displacement of the object. [Sci Pr 2.2]


Science Practices and Laboratory Requirements

The lab requirements listed below for each course are very similar in that with the creation of the AP

Physics I course, the science practices listed below and referenced the learning objectives above

encompass all the science objectives in the Mechanics C course with a mandate to increase the reliance

upon Inquiry and Guided Inquiry labs and activities to enhance student understanding and insight.

AP Physics C Mechanics AP Physics I These objectives overlay the content objectives, and

are assessed in the context of those objectives.

1. Design experiments

Students should understand the process of designing

experiments, so they can:

a) Describe the purpose of an experiment or a

problem to be investigated.

b) Identify equipment needed and describe how it is

to be used.

c) Draw a diagram or provide a description of an

experimental setup.

d) Describe procedures to be used, including controls

and measurements to be taken.

2. Observe and measure real phenomena

Students should be able to make relevant

observations, and be able to take measurements with

a variety of instruments (cannot be assessed via

paper-and- pencil examinations).

3. Analyze data

Students should understand how to analyze data, so

they can:

a) Display data in graphical or tabular form.

b) Fit lines and curves to data points in graphs.

c) Perform calculations with data.

d) Make extrapolations and interpolations from data

4. Analyze errors

Students should understand measurement and

experimental error, so they can:

a) Identify sources of error and how they propagate.

b) Estimate magnitude and direction of errors.

c) Determine significant digits.

d) Identify ways to reduce error.

5. Communicate results

Students should understand how to summarize and

communicate results, so they can:

a) Draw inferences and conclusions from

experimental data.

b) Suggest ways to improve experiment.

Science Practice 1: The student can use representations and models to communicate scientific phenomena and solve scientific problems Science Practice 2: The student can use mathematics appropriately Science Practice 3: The student can engage in scientific questioning to extend thinking or to guide investigations within the context of the AP course Science Practice 4: The student can plan and implement data collection strategies in relation to a particular scientific question Science Practice 5: The student can perform data analysis and evaluation of evidence Science Practice 6: The student can work with scientific explanations and theories Science Practice 7: The student is able to connect and relate knowledge across various scales, concepts, and representations in and across domains


c) Propose questions for further study.

Explanation of Areas that are Specific to Physics C Mechanics

Those learning objectives highlighted in the table above are the 10 specific LO’s that are not

overlapping in these two curricula in that they are the objectives that require the use of calculus. These

Math Science Academy students will have already mastered the actual calculus requirements and these

Objectives will be an application of the calculus to the physics situations.

The AP Physics I course was developed to be an algebra based physics course that is rich in

conceptual development and explanation, with somewhat limited requirement of numerical calculations

to solve problems. While many problems involve calculations, the answers are most often required in

terms of algebraic variables rather than numbers. The AP Physics C Mechanics course also has many

questions that require this sort of answer as well. In fact, I have used many of the available Physics C

Mechanics questions as quiz and test questions in my AP Physics I course by deleting the parts of

questions requiring for calculus and with little or no other modification required.

The use of AP Physics C Mechanics Multiple choice questions on test or for review is also

something that was easily accomplished as they are very similar to the sample items released by the

College Board.

In essence, the AP Physics I course is a very complete and fundamental treatment of all the

areas of Mechanics with a focus on conceptual understanding of situations and relationships.

Combining this with the rigorous mathematical treatment mandated by the AP Physics C mechanics

course will give these Math and Science Academy students a complete understanding of Newtonian

Mechanics both mathematically and conceptually and will give them the advantage of accomplishing

this mastery in only one school year.

investing in educational excellence (ie · lo(3.a.3.1): the student is able to analyze a scenario...

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