Question

A ball is hanging on the end of a string which is being swung such that the ball follows a circular path, performing 54.1 revolutions in 0.6 seconds. What is its angular velocity?

Answer 1

Angular velocity is defined as

$\omega = 2\pi f$

now we know that

frequency = number  of revolutions per seconds

here we know that

N = 54.1 revolutions

t = 0.6 s

now from above definition we know that

$f = \frac{N}{t}$

$f = \frac{54.1}{0.6} = 90.17 rev/s$

now from above equation

$\omega = 2\pi f$

$\omega = 2\pi(90.17)$

$\omega = 566.1 rad/s$