# An object with a mass of 7 kg is revolving around a point at a distance of 7 m. If the object is making revolutions at a frequency of 9 Hz, what is the centripetal force acting on the object?

Jan 9, 2018

OK, there are two equations for centripetal force, both useful, we need the one that has $\omega$ in it as we are given a frequency, not a linear velocity.

#### Explanation:

The equations are:

$F = \frac{m {v}^{2}}{r}$ and $F = m {\omega}^{2} r$ where $\omega = 2 \pi f$ and is called the angular velocity (but confusingly, also the angular frequency.)

First, we find $\omega = 2 \pi f = 2 \times 3.14 \times 9 = 56.52$ rad/s

Next the force, $F = m {\omega}^{2} r = 7 \times \left({56.52}^{2}\right) \times 7 = 156 531$N

I’d quote this as $F = 160 , 000$N given the data you have.