{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson_2.4_Printable

# Lesson_2.4_Printable - Circular Motion Consider an object...

This preview shows pages 1–5. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 . Here r is the radius of the circle. -1 m s s v t = s r v = r ϖ gives a relation between linear speed and angular velocity. The time taken by the object to go round the circle once is called its period ( T ) During this time T , the angle described is 2 π radians r v t θ = r t = r ϖ = -1 2 = rad s T t 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 the frequency is Hz e period = 1/5 s If an object goes round a circle 5 times a second, its frequency f = 5 Hz . s r If the frequency is 5 Hz , the period T = 1/5 s Can you figure out why this is so? Frequency and period are related such that one is the reciprocal of the other. 1 T f = 1 T f = f T = 1 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A Since the direction of motion of an object in circular motion is changing continuously, its velocity changes continuously. B Velocity is a vector quantity. It has magnitude and direction O θ The direction of velocity at any instant is along the tangent to the circle r v 1 v 2 v At point A, the velocity is v 1 . At point B the velocity is v 2 . v 1 and v 2 differ only in direction. They have equal magnitudes.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 20

Lesson_2.4_Printable - Circular Motion Consider an object...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online