Question

A 6.5-kg bowling ball is being swung horizontally in a clockwise direction (as viewed from above) at a constant speed in a circle of radius 1.5 m.Suppose the time it takes the ball to make one complete revolution is 2.75 s. What is the centripetal acceleration of the ball?

Answer 1

`a_c=7.83(m)/(s^2)`

Step-by-step explanation:

Centripetal acceleration is defined as:

`a_c=(v^2)/(r)(1)`

Here v is the linear speed and r is the radius of the circular motion. The linear speed are given by:

`v=\omega r(2)`

The angular speed is defined as:

`\omega=(2\pi)/(T)(3)\\`

Replacing (3) in (2):

`v=(2\pi r)/(T)(4)`

Finally, we replace (4) in (1):

`a_c=(((2\pi r)/(T))^2)/(r)\\\\a_c=(4\pi^2 r)/(T^2)\\a_c=(4\pi^2(1.5m))/((2.75s)^2)\\a_c=7.83(m)/(s^2)`