Solved Examples

1.    A particle moves in a circle of radius 20 cm with a linear speed of 10 m/s. Find the angular velocity.
Sol.    The angular velocity is 
2.    A particle travels in a circle of radius 20 cm at a speed that uniform increses. If the speed changes from 5.0 m/s to 6.0 m/s in 2.0s, find the angular acceleration.
Sol.    The tangentical accelaration is given by
3.    Find the magnitude of the linear acceleration of a particle moving in a circle of radius 10 cm with uniform speed completing the circle in 4s.
Sol.    The distance covered in completing the circle is 2r = 2 × 10 cm.The linear speed is
4.    A particle moves in a circle of radius 20 am. Its linear speed is given by v = 2t where t is in second  and v in meter/second . Find the radical and tangential acceleration at t = 3s.
Sol.    The linear speed at t  = 3s is 
                       v  = 2t  = 6 m/s.
    The radical acceleration at t  = 3s is 
                 ar =  v2 / r = 36/0.20 = 180 m/s2.                     
    The tangent acceleration is 
                 at =dv/dt  = d(2t)/dt = 2 m/s2.  

5.    A small block of mass 100 g moves with uniform speed in a horizontal circular groove, with vertical  side walls , of radius 25 cm. If the block takes 2.0s to complete one round, find the normal contact force by the slide wall of the groove.
Sol.    The speed of the block is

6.    The  road at a circular turn of radius 10m is banked by an angle of 10º. With what speed should a vehicle move on the turn so that the normal contact force is able to provide the necessary force ?
Sol.    If v is the correct speed
7.    A body weighs 98N on a spring balance at the

north pole. What will be its weight recorded on the same scale if it is shifted to the equator? Use g = GM/R2 = 9.8 m/s2 and the radius of the earth R=6400 km.
Sol.    At poles , the apparent weight is same as the true weight.


Questions for Short Answer

1.    You are driving a moorcycle on a horizontal road. It is moving with a  uniform velocity. Is it possible to accelerate the motorcycle without putting higher petrol input rate into the engine ?

2.    Some washing machines have cloth driers. It contains a drum in which wet clothes are kept. As the drum rotates, the water particles get separated from the cloth. The genral description of this action is that “the contrifugal force throws the water particles away from the drum”. Comment on this statement from the view-point of an observer rotating with the drum and the observer who is washing the clothes.  

6.    After a good metal at a party you wash your hands and  find that you have forgotten to bring your handker chief.

7.    A  smooth block loosely fits in a circular