⇒ Graphs: ⇒ Direct Relationship: Linear ⇒ Inverse Relationship: Hyperbola ⇒ Quadratic Relationship: Parabola

⇒ Kinematics: study of motion and the relationships between time, distance, and speed ⇒ Velocity: a vector quantity; has magnitude and direction; it is the time rate of change of position in

a certain direction ⇒ Velocity is the slope of a displacement-time graph

⇒ Instantaneous Speed: slope of the tangent in a distance-time graph ⇒ Acceleration: time rate of change of velocity

⇒ When a body changes velocity, it is said to have variable motion ⇒ Displacement: the area between the curve and the time axis in a velocity-time graph ⇒ When gravity is the only force, bodies accelerate at the same rate regardless of mass and hit the

ground at the same time and the same speed ⇒ In the absence of air resistance, an object will accelerate on earth at 9.8 m/s2 ⇒ Air Resistance: as a body falls near the surface of the Earth, the force of gravity remains constant

and the air resistance increases as the speed increases; terminal velocity is reached when the lift is equal to the weight

⇒ Vertical Motion: gravity decelerates objects on the way up and accelerates them on the way down; gravity is the same on the way up and the way down so the change of speed is the same as well

⇒ Vup = Vdown with a change in direction ⇒ Time up = Time down

⇒ Pendulum: ⇒ Speed at the top is 0 m/s ⇒ Speed at the bottom is the maximum ⇒ Period is independent of the amplitude (size of swing)—angle ⇒ Period is independent of the mass—all objects fall at the same rate ⇒ Period is directly proportional to the length of the pendulum ⇒ Always tries to reach the same height

⇒ Force: that which causes a push or a pull ⇒ If an object moves at some constant speed and no force is present, then the object is in

uniform motion ⇒ If a force is present, then the object will change velocity and the motion is variable ⇒ When objects do not change speed, the motion is uniform

⇒ Newton’s First Law of Motion: every body continues in its state of rest or at uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it

⇒ Principle of Inertia: inertia is the property of a body to resist a change in motion ⇒ Frame of Reference: all motion is described from a position considered to be at rest or at a

constant velocity ⇒ Equilibrium: a body is in equilibrium when there is no net force; forces cancel each other

out, forces are balanced, no acceleration ⇒ Newton’s Second Law of Motion: the effect of an applied net force is to cause the body to

accelerate in the direction of the net force; the acceleration is in direct proportion to the net force and in inverse proportion to the mass of the body

⇒ Mass: measure of the quantity of matter—value is constant ⇒ Weight: force due to gravity which depends on the acceleration due to gravity (g) where Fg = mg

⇒ Friction: a force that acts parallel to the surfaces that are in contact and in the direction opposite to the force producing or tending to produce motion

⇒ Sliding (also called kinetic or moving) friction is less than starting (also called static) friction ⇒ Friction is independent of area of contact ⇒ Friction is independent of speed of the surfaces in contact ⇒ Friction is directly proportional to the force pressing the two surfaces together (FN)

⇒ Newton’s Third Law of Motion: to every action there is always an opposed and equal reaction; implies that forces always occur in pairs between objects in the universe

⇒ The acceleration of each object depends upon the mass of the object since the forces are the same for both

⇒ Elevators: ⇒ When it accelerates, for a fraction of a second, FN increases ⇒ When it decelerates as it comes to a stop, FN decreases ⇒ *At rest and at constant speed, FN = Fg

⇒ 2D Forces: to resolve a force is to break it down into its component forces (x and y components) so that the component forces have the same effect as the original force

⇒ Horizontal Projectile: ⇒ x-direction: constant speed, explained by the absence of a force ⇒ y-direction: increasing speed, caused by unbalanced forces (Fg) ⇒ Projectile: object under the influence of gravity only ⇒ Trajectory: the path followed by a projectile flying or an object moving under the action of

given forces ⇒ All objects fall with the same acceleration

⇒ Projectiles at Angles: ⇒ Horizontal Motion: constant speed because the vectors have equal lengths; inertia keeps

the projectile moving forward ⇒ Vertical Motion: vertical speed decreases on the way up, is 0 at the top, and increases on

the way down; acted upon by Fg ⇒ At 45º, the projectile goes the furthest distance

⇒ Uniform Circular Motion: objects move at constant speed in a circular path ⇒ Revolution: when an object turns about an external axis (ex: Earth around the Sun) ⇒ Rotation: when an object turns about an internal axis (ex: ice skater performing a spin) ⇒ Centripetal Force: force necessary for an object to move in a circular path; directed toward the

center ⇒ The feeling of being pulled outward is due to the object trying to continue in a straight line

at constant speed (inertia) ⇒ If the centripetal force is eliminated, the object will move at a constant speed in a straight

line tangent to the circle ⇒ Newton’s Law of Universal Gravitation: any two bodies in the universe attract each other with a

force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

⇒ Astronauts experience weightlessness in orbit because the shuttle is always free falling at all times

⇒ ‘g’ is less at the Equator than at the North Pole because the Earth bulges at the Equator ⇒ At the top of a mountain, ‘g’ decreases ⇒ If the distance to the center of the planet increases, then ‘g’ decrease

⇒ Kepler’s First Law of Planetary Motion: the paths of planets are ellipses with the Sun at one focus

⇒ Kepler’s Second Law of Planetary Motion: an imaginary line from the Sun to a planet sweeps out equal area in equal time intervals

⇒ Planets move the fastest when closest to the Sun and they move slower when further away ⇒ Kepler’s Third Law of Planetary Motion: (TA/TB)2 = (RA/RB)3

⇒ Planets, objects must be going around the same thing ⇒ Period: time for one revolution

⇒ Momentum: measure of the quantity of motion; product of mass and velocity ⇒ Impulse: measure of the amount of force acting over a period of time; product of force and the

amount of time the force is applied ⇒ Impulse causes a change in motion meaning a change in momentum. A negative value of

force indicates that it is in the opposite direction of motion ⇒ Newton’s Second Law can be rearranged to show that impulse causes a change in

momentum ⇒ Collisions: Athletes depend on change in momentum to excel in their sports; to decrease the

momentum of a moving object, the time of contact can be increased to reduce the impact force ⇒ Hard Collisions: big force and short impact time ⇒ Soft Collisions: small force and longer impact time

⇒ Law of Conservation of Momentum: when two bodies collide, the total momentum of the whole system before the collision is equal to the total momentum of the whole system after the collision

⇒ Elastic Collision: the colliding bodies don’t stick together ⇒ Inelastic Collision: the colliding bodies stick together ⇒ Momentum is conserved, not velocity

⇒ Work: process of transferring energy; work is done when a force acts on a body and produces motion in the direction of the force

⇒ Power: time rate of doing work (how fast the work can be done) or the rate at which energy can be transformed

⇒ Energy: the capacity to do work ⇒ Conservation of Energy: the total amount of energy in a closed system will never change ⇒ Potential Energy: energy that is “stored”

⇒ As long as an object is above the reference point, it has potential energy ⇒ Gravitational Potential Energy: when work is done against the force of gravity,

there is an increase in the potential energy of the object ⇒ Elastic Potential Energy: when a person does work against an elastic force, then

you increase the potential energy of the object ⇒ Kinetic Energy: energy due to the motion of the body ⇒ *For forces that are not constant, work equals the area under the curve of a force-work

graph ⇒ If work causes the object to change position or shape, then the object gains/loses potential

energy ⇒ If work causes the object to change speed, then the object gains/loses kinetic energy

⇒ Conservation of Energy: ⇒ If only conservative forces are acting, the total mechanical energy of a system neither

increases nor decreases in any process; it stays constant—it is conserved ⇒ In a collision, mechanical energy is not necessarily conserved; some energy might be lost to

heat—in this case using conservation of momentum is helpful in solving the problem ⇒ If the kinetic energy is conserved, the collision is said to be elastic

⇒ Forces for which the work done does not depend on the path taken are Conservative Forces (ex: gravity, spring)

⇒ The work done by non-conservative forces depends on the path taken (friction) ⇒ Work done by Ff or air resistance is negative

⇒ Work-Energy Theorem: the net work done on an object is equal to the change in kinetic energy of the object

⇒ Springs: ⇒ A mass oscillating on a spring exhibits simple harmonic motion; the force in the spring will

act as a restoring force, which is directly proportional to the distance stretched/compressed from equilibrium, meaning the further you stretch/compress the spring, the greater the restoring force

⇒ Period of a Pendulum: ⇒ Higher acceleration of gravity à shorter period ⇒ Lower acceleration of gravity à longer period ⇒ Period of an oscillating mass on a spring is not affected by the acceleration of gravity

⇒ Angular Distance: the angle (in radians) a body rotates ⇒ Angular Speed: the time rate change of angular distance ⇒ Angular Acceleration: time rate change of angular speed ⇒ Torque: (moment of the force); cause of rotational motion; twisting effect of a force

⇒ A net force makes an object accelerate; a net torque makes an object rotate ⇒ To increase torque, increase force, increase lever arm, or get the angle close to or equal to

90 ⇒ Torque is maximized at the largest distance from the axis of rotation

⇒ Rotational Equilibrium: state of a system where the counterclockwise torques are balanced by the clockwise torques

⇒ Center of Mass (Gravity): ⇒ To increase stability, lower one’s center of mass or enlarge one’s base ⇒ The center of gravity may be inside or outside the body ⇒ A body spins around its center of gravity ⇒ Objects balance at their center of gravity

⇒ Rotational Mass (Inertia): the way a body rotates depending on its distribution of mass ⇒ The higher the rotational inertia à lazier

⇒ Newton’s Second Law for Rotational Motion: the angular acceleration of a body is directly proportional to the amount of torque and inversely proportional to its rotational mass

⇒ Conservation of Angular Momentum: ⇒ The total angular momentum of a rotating body remains constant if the net torque acting

on it is zero (Li = Lf if the net torque = 0) ⇒ A torque applied over a period of time will change the angular momentum of a rotating

body