# A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s. a) Calculate the angular displacement of the bowling ball. b) Calculate the angular velocity of...

A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.

a) Calculate the angular displacement of the bowling ball.

b) Calculate the angular velocity of the bowling ball

c) Calculate the radial acceleration of the bowling ball.

d) Calculate the tangential acceleration of the bowling ballĀ

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### 1 Answer

When a round symmetric rigid body like a bowling ball of radius R rolls without slipping on a horizontal surface, the distance through which its center travels (when the sphere in motion, turns by an angle theta) is the same as the arc length through which a point on the edge moves.

Therefore,

a) Angular displacement, theta =arc length/R=10/0.09=111.1 radians

b) The speed of the center of mass of the rolling ball and its angular velocity are related by

`v=R*omega`

`omega=v/R=4.3/0.09` , i.e. 47.78 rad/s

Similarly, the acceleration of the center of mass is related to the angular acceleration as:

`a=Ralpha`

c) Acceleration of the center of mass, or radial acceleration, `a=omega^2*R=47.78^2*0.09=205.4` rad/s^2

d) As the ball does not skid, its acceleration is inward. So its tangential acceleration is zero.