# 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 ball

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### 1 Answer

a) You need to evaluate the angular displacement of the ball, using the following formula, such that:

`theta = S/r`

The displacement S = 10 m, and the radius r = 9 cm, hence, you need to convert the units of measure, such that:

`r = 9cm = 9*10^(-2) = 0.09 m`

`theta = 10/0.09 = 111 ` rad

b) You need to evaluate the angular velocity using the following formula, such that:

`omega = v/r => omega = 4.3/0.09 = 47.77 (rad)/s`

c) You need to evaluate the radial acceleration using the following formula, such that:

`a = v^2/r => a = (4.3)^2/(0.09) = 205.4 (rad)/s^2`