2. 1© Manhattan Press (H.K.) Ltd. Angular displacement (  ) Angular velocity (  ) Angular velocity (  ) 5.1 Angular velocity and linear velocity Linear velocity (v) Linear velocity (v)

3. 2 © Manhattan Press (H.K.) Ltd. Angular displacement (  ) 5.1 Angular velocity and linear velocity (SB p. 165) Move in a circle from A to B - radius (r) subtends an angle  - length of arc (s) in radian  - angular displacement

4. 3 © Manhattan Press (H.K.) Ltd. Angular velocity (  ) 5.1 Angular velocity and linear velocity (SB p. 165) Angular velocity (  ) – rate of change of angular displacement in rad s -1 or rev min -1 or rev s -1 Note: The unit radian is only a ratio of length (dimension) and sometimes it can be omitted. For example, unit of  may be rad s –1 or s –1. Instantaneous angular velocity (as t  0)

5. 4 © Manhattan Press (H.K.) Ltd. Angular velocity (  ) 5.1 Angular velocity and linear velocity (SB p. 166) 1. Period (T) - time taken complete rotation

6. 5 © Manhattan Press (H.K.) Ltd. Angular velocity (  ) 5.1 Angular velocity and linear velocity (SB p. 166) 2. Frequency (f) - no. of rotations per second  = 2  f angular frequency

7. 6 © Manhattan Press (H.K.) Ltd. Linear velocity (v) 5.1 Angular velocity and linear velocity (SB p. 166) v = r  direction: tangent to path of circular motion, is changing Go to Example 1 Example 1 Go to Example 2 Example 2

8. 7 © Manhattan Press (H.K.) Ltd. End

9. 8 © Manhattan Press (H.K.) Ltd. Q: Q:A phonograph record rotates at revolutions per minute. (a) Express the angular velocity of the record in radians per second. (b) What are the speeds of a lady bird sitting on the record at a distance of (i) 5.0 cm, and (ii) 10.0 cm from the centre of the circular motion? Solution 5.1 Angular velocity and linear velocity (SB p. 167)

10. 9 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 5.1 Angular velocity and linear velocity (SB p. 167) (b) (i) Using v = r  = 5.0 ×3.49 = 17.45 cm s –1 (ii) v = 10.0 ×3.49 = 34.9 cm s –1

11. 10 © Manhattan Press (H.K.) Ltd. Q: Q:(a) (i) If an angle θ equals 1 radian, what is its value in degrees? (ii) If a body moving in a circle subtends an angle of 1 radian with radius r = 5 cm, what is its arc l ength? (b) What is the angular velocity of the second hand of a watch? (c) A boy stands at the equator of the earth. Find (i) his angular velocity, and (ii) his linear speed. (1 day = 8.6 × 10 4 s, radius of earth = 6.38 × 10 6 m) Solution 5.1 Angular velocity and linear velocity (SB p. 168)

12. 11 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 5.1 Angular velocity and linear velocity (SB p. 168)