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

Answer:

$a_c=7.83\frac{m}{s^2}$

Explanation:

Centripetal acceleration is defined as:

$a_c=\frac{v^2}{r}(1)$

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:

$\omega=\frac{2\pi}{T}(3)$

Replacing (3) in (2):

$v=\frac{2\pi r}{T}(4)$

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

$a_c=\frac{(\frac{2\pi r}{T})^2}{r}\\\\a_c=\frac{4\pi^2 r}{T^2}\\a_c=\frac{4\pi^2(1.5m)}{(2.75s)^2}\\a_c=7.83\frac{m}{s^2}$