CIRCULAR MOTION Angular Motion Angular displacement Angular velocity

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 bodies • 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 corner • Bicycle turning in a smooth banked 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] • Suspended particle in a vertical circle [Figure] • The outside of a smooth vertical circular rod [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]

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 5 r/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