CIRCULAR MOTION
Angular Motion Angular displacement: Angular velocity: Angular acceleration Uniformly accelerated motion
Linear Vs Angular Kinematics
Period: T Frequency: f
Relation between Tangential and Angular Velocities
Uniform Circular Motion Tangential acceleration: Centripetal (Normal) acceleration:
Centripetal Force A resultant force acting towards the centre Centripetal acceleration Centripetal force:
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
Experimental Verification Computer simulation
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
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
Conical Pendulum
Motion of Cyclist Round Circular Track Condition for skidding: tan > is independent of m In turning a sharp corner, must be large
Motion of Car round Circular Track Car will overturn if Car will skid if
Banking For no side-slip at the wheels Daily example: racing track
Aircraft Turning in Flight Banking angle for the turn:
Centrifuge To separate particles in suspension from the less dense liquid Procedure
Rotor The person will not slip down if
Variation of g with Latitude g’ = g - r 2
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
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
Bucket of Water Whirled in a Vertical Circle For the water to stay in the bucket:
Looping the loop To describe a complete circle: h 5r/2
Examples
Orbits Back
Turning Round a Corner Centripetal force is provided by the frictional force between the wheels and the road Back
Banked Track in Cycling Centripetal force is provided by the horizontal component of the normal reaction. Back
Ring Threaded on a Smooth Vertical Circular Wire Back
Suspended Particle in a Vertical Circle Back
The Outside of a Smooth Vertical Circular Rod Back
Conditions for Describing a Complete Vertical Circle Back