Lesson 2.4 Circular Motion

# Lesson 2.4 Circular Motion - Circular Motion Consider an...

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Circular Motion A It moves along the arc of a circle of radius OA to position B B Consider an object at the point A on the line OA O The line OB makes an angle θ with the original line OA θ When the object moves from A to B, along the circular path, the radius rotates through an angle θ from position OA to OB. If this angle θ is described in a time t, the rate at which this angle is described is given by θ /t Angle θ is called the angular displacement of the object The rate of change of angular displacement of an object in circular motion is called its angular velocity ( ϖ ) -1 rad s t θ ϖ= ϖ is measured in radian per second. 1

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Relation between angular velocity and linear speed A The linear speed of the object along this path is: B The length of the path ( s ) of the object is the distance measured from A to B along the curve. O θ But s = r θ . v = r ϖ gives a relation between linear speed and angular velocity. Here r is the radius of the circle. The time taken by the object to go round the circle once is called its period ( T ) -1 m s s v t = During this time T , the angle described is 2 π radians s r r v t θ = r t = r ϖ = -1 2 = rad s T t π ϖ= 2 T 2
Frequency and Period A Frequency f is measured in a unit called hertz ( Hz ). This is the same as per second ( s -1 ): B The number of times the object goes round the circle in one second is called its frequency ( f ). O θ If the frequency is 5 Hz , the period T = 1/5 s If an object goes round a circle 5 times a second, its frequency f = 5 Hz . Can you figure out why this is so? Frequency and period are related such that one is the reciprocal of the other. s r 1 T f = 1 T f = f T = 1 3

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Acceleration of circular motion A Since the direction of motion of an object in circular motion is changing continuously, its velocity changes continuously. Velocity is a vector quantity. It has magnitude and direction O The direction of velocity at any instant is along the tangent to the circle At point A, the velocity is v 1 .
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## This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

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Lesson 2.4 Circular Motion - Circular Motion Consider an...

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