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.
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