rene descartes (1736-1806)
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DESCRIPTIONMotion In Two Dimensions. RENE DESCARTES (1736-1806). GALILEO GALILEI (1564-1642). Vectors in Physics. All physical quantities are either scalars or vectors. Scalars. A scalar quantity has only magnitude. - PowerPoint PPT Presentation
RENE DESCARTES(1736-1806)Motion In Two DimensionsGALILEO GALILEI(1564-1642)
Vectors in PhysicsA scalar quantity has only magnitude.All physical quantities are either scalars or vectorsA vector quantity has both magnitude and direction.ScalarsVectorsCommon examples are length, area, volume, time, mass, energy, voltage, and temperature.Common examples are acceleration, force, electric field, momentum.In kinematics, distance and speed are scalars.In kinematics, position, displacement, and velocity are vectors.
Representing VectorsThe arrows length represents the vectors magnitudeA simple way to represent a vector is by using an arrow.The arrows orientation represents the vectors directionStandardAngleBearingAngle090180270E, 90N, 0W, 270S, 180In physics, a vectors angle (direction ) is called theta and the symbol is . Two angle conventions are used:
Vector MathVector EquivalenceTwo vectors are equal if they have the same length and the same direction.Two vectors are opposite if they have the same length and the opposite direction.Vector Oppositesequivalence allows vectors to be translatedopposites allows vectors to be subtracted
click for appletHead to Tail AdditionVectors add according to the Head to Tail rule.The tail of a vector is placed at the head of the previous vector.The resultant vector is from the tail of the first vector to the head of the last vector. (Note that the resultant itself is not head to tail.)For the Vector Field Trip, the resultant vector is 68.6 meters, 79.0South Lawn Vector Walkclick for web site
Graphical Addition of VectorsVector AdditionVectors add according to the Head to Tail rule. The resultant vector isnt always found with simple arithmetic!click for appletclick for appletsimple vectoradditionright trianglevector additionnon-right trianglevector additionVector SubtractionTo subtract a vector simply add the opposite vector.simple vectorsubtractionright trianglevector subtraction
Resolving VectorsIt is useful to resolve or break down vectors into component vectors.(Same as finding rectangular coordinates from polar coordinates in math.)
Finding a ResultantOften a vectors components are known, and the resultant of these components must be found.(Same as finding polar coordinates from rectangular coordinates in math.)Finding the magnitude of the resultant:Finding the direction of the resultant:
Resolving VectorsExample: A baseball is thrown at 30 m/s at an angle of 35 from the ground. Find the horizontal and vertical components of the baseballs velocity.Horizontal velocity:Vertical velocity:
Finding a ResultantExample: A model rocket is moving forward at 10 m/s and downward at 4 m/s after it has reached its peak. What overall velocity (magnitude and direction) does the rocket have at this moment?Find the rockets speed (magnitude)Find the rockets angle (direction)
Projectile MotionHorizontal:constant motion, ax = 0Vertical:freefall motion,ay = g = 9.8 m/s2velocity is tangent to the path of motionclick for appletclick for appletProjectile motion =constant motion +freefall motionresultant velocity:
Projectile Motion at an Angleclick for appletclick for appletvelocity components:vertical velocity, vy is zero here!
Relative VelocityAll velocity is measured from a reference frame (or point of view).Velocity with respect to a reference frame is called relative velocity.A relative velocity has two subscripts, one for the object, the other for the reference frame.Relative velocity problems relate the motion of an object in two different reference frames.refers tothe objectrefers to thereference frameclick for reference frame appletclick for relative velocity appletvelocity of object a relative to reference frame bvelocity of reference frame b relative to reference frame cvelocity of object a relative to reference frame c
Relative VelocityAt the airport, if you walk on a moving sidewalk, your velocity is increased by the motion of you and the moving sidewalk. vpg = velocity of person relative to groundvps = velocity of person relative to sidewalkvsg = velocity of sidewalk relative to groundWhen flying against a headwind, the planes ground speed accounts for the velocity of the plane and the velocity of the air.vpe = velocity of plane relative to earthvpa = velocity of plane relative to airvae = velocity of air relative to earth
Relative VelocityWhen flying with a crosswind, the planes ground speed is the resultant of the velocity of the plane and the velocity of the air.vpe = velocity of plane relative to earthvpa = velocity of plane relative to airvae = velocity of air relative to earthSometimes the vector sums are more complicated!Pilots must fly with crosswind but not be sent off course.