# Centripetal Force of a Ball Revolving Uniformly in a Horizontal Circle

Date of Exam:

**Problem**

A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

A. 74.95 m/sec^{2} |
C. 49.57 m/sec^{2} |

B. 94.75 m/sec^{2} |
D. 59.47 m/sec^{2} |

**Answer Key**

[ B ]

**Solution**

**Angular Speed**

$\omega = 2 ~ \dfrac{\text{rev}}{\text{sec}} \cdot \dfrac{2\pi ~ \text{rad}}{\text{rev}} = 4\pi ~ \text{rad/sec}$

**Linear Speed**

$v = r\omega = 0.6(4\pi) = 2.4\pi ~ \text{m/sec}$

**Centripetal Acceleration**

$a_c = \dfrac{v^2}{r} = \dfrac{(2.4\pi)^2}{0.6}$

$a_c = 94.79 ~ \text{m/sec}^2$ ← *answer*