Question

A 7.25-kg bowling ball is being swung horizontally in a clockwise direction (as viewed from above) at a constant speed in a circle of radius 1.85 m.1. Suppose the time it takes the ball to make one complete revolution is 2.75 s. What is the centripetal acceleration?

Answer 1

Answer:

$a_c=9.66\frac{m}{s^2}$

Explanation:

The centripetal acceleration is given by:

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

Here v is the linear speed and r is the radius of the circular motion. v is defined as the distance traveled to make one revolution ($2\pi r$) divided into the time takes to make one revolution, that is, the period (T).

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

Replacing (2) in (1) and replacing the given values:

$a_c=\frac{(\frac{2\pi r}{T})^2}{r}\\a_c=\frac{4\pi^2 r}{T^2}\\a_c=\frac{4\pi^2 (1.85m)}{(2.75s)^2}\\a_c=9.66\frac{m}{s^2}$