Circular Motion Chapter 7.3

Motion & Forces What you already know: –Velocity – a measure of the change in over with. –Mass – A measure of the amount of an object contains. –Acceleration – A measure of the change in over change in. –Force – A or that is equal to the mass of the object multiplied by its acceleration (F = _____).

Uniform Circular Motion Uniform circular motion is defined by any object that is moving at in a circular path. –Determining : »The distance an object moving in a circular path is equal to the (__ = _____). »The time it takes an object to complete one revolution is called the (___). »It then follows that the speed of an object moving in a circular path can be determined by: v =

Uniform Circular Motion If an object is moving at constant speed in a circular path, can it be accelerating? – »Although the speed may be, the is. »If is changing over time, then the must be changing. » is the change in over (___ = ___). »If the is changing over time, then the object must be. v v v v

Circular Motion – Instantaneous Velocity Note that the vector is at to the vector and to the circle at any given point along the circle. v1v1 v2v2  r1r1 r2r2  r1r1 r2r2 rr v =  r/  t

Circular Motion – Centripetal Acceleration (a c ) The of an object moving in a circular path always __________ ____________ _____ __________ ___ ____ ___________, and is perpendicular to the velocity vector. v1v1 v2v2 r a a =  v/  t  v v v2v2 -v 1   v v

Centripetal Acceleration The angle between r 1 and r 2 is the same as the angle between v 1 and v 2. –Therefore, the triangles these vectors make are such that: = –If you divide both sides by ___: = –Where : » = v and = a –Hence: = and =

Centripetal Acceleration An alternative representation for centripetal acceleration can be derived using the and period of. »d = »v = –Substituting into a c = »a c =

Circular Motion – Force To make an object move in a circular path, an must act or at right angles to its of. This force is called. direction of velocity Direction of required to make object move in a circular path ()

Centripetal Force Centripetal force is affected by: –The of the object (___). –The of the object around the circle (___). –The of the circle (___). Using Newton’s 2 nd Law of Motion (F c = ma c ), centripetal force is mathematically represented as follows: Note: Centripetal force is an “ ” force FcFc

How the Factors Affect Centripetal Motion Which graph shows the proper relationship with respect to force: –Force vs. Mass. –Force vs. Speed. –Force vs. Radius. Speed Radius Mass

Objects that travel in circular paths. What is the cause of the force? The Earth – Sun System: –. A racecar traveling around a turn on the racetrack: –. An athlete throwing the hammer: –.

The path of objects. If the centripetal force were suddenly removed from an object moving in a circular path, what trajectory (or path) would it follow?

Which Path? (a) (b) (c)

Which Path? Why does the object travel in a straight path once the centripetal force is gone? – Because of – An object in wants to in at in a. – If the is removed, the object will continue in a straight path.

Example #1: A 1.5 kg cart moves in a circular path of 1.3 meter radius at a constant speed of 2.0 m/s. –Determine the magnitude of the centripetal acceleration. –Determine the magnitude of the centripetal force. –Determine the period.

Example #1: (cont.) Centripetal Acceleration: a c = Centripetal Force: F c = Period: T =