2. CIRCULAR MOTION

3. Angular Motion Angular displacement:  Angular velocity: Angular acceleration Uniformly accelerated motion

4. Linear Vs Angular Kinematics

5. Period: T Frequency: f

6. Relation between Tangential and Angular Velocities

7. Uniform Circular Motion Tangential acceleration: Centripetal (Normal) acceleration:

8. Centripetal Force A resultant force acting towards the centre Centripetal acceleration Centripetal force:

9. Conclusion Not a new type of force Force  velocity Centripetal force does not imply the object will move to the centre of the circle Experimental verification The force does no work on the object If the force ceases to act, the object will move off tangentially

10. Experimental Verification Computer simulation

11. Examples of Circular Motion Orbital motion of satellites and heavenly bodiesOrbital motion Spinning of machine parts or wheels Motion of charged particles in a magnetic field Early models of atoms

12. Further Examples Turning of a vehicle round a cornerround a corner Bicycle turning in a smooth banked trackbanked track Liquid spinning in a bucket about a vertical axis Aircraft turning in flight

13. Conical Pendulum

14. Motion of Cyclist Round Circular Track Condition for skidding: tan  >   is independent of m In turning a sharp corner,  must be large

15. Motion of Car round Circular Track Car will overturn if Car will skid if

16. Banking For no side-slip at the wheels Daily example: racing track

17. Aircraft Turning in Flight Banking angle for the turn:

18. Centrifuge To separate particles in suspension from the less dense liquid Procedure

19. Rotor The person will not slip down if

20. Variation of g with Latitude g’ = g - r  2

21. Motion in a Vertical Circle Ring threaded on a smooth vertical circular wire [Figure]Figure Suspended particle in a vertical circle [Figure]Figure The outside of a smooth vertical circular rod [Figure]Figure

22. Conditions of Describing a Complete Vertical Circle Case I: the particle is suspended by a light rigid rod Case II: the particle is suspended by a light string [Figure]Figure

23. Bucket of Water Whirled in a Vertical Circle For the water to stay in the bucket:

24. Looping the loop To describe a complete circle: h  5r/2

25. Examples

26. Orbits Back

27. Turning Round a Corner Centripetal force is provided by the frictional force between the wheels and the road Back

28. Banked Track in Cycling Centripetal force is provided by the horizontal component of the normal reaction. Back

29. Ring Threaded on a Smooth Vertical Circular Wire Back

30. Suspended Particle in a Vertical Circle Back

31. The Outside of a Smooth Vertical Circular Rod Back

32. Conditions for Describing a Complete Vertical Circle Back