# An object with a mass of 6 kg is revolving around a point at a distance of 8 m. If the object is making revolutions at a frequency of 6 Hz, what is the centripetal force acting on the object?

Jul 10, 2016

The force acting on the object is $6912 {\pi}^{2}$ Newtons.

#### Explanation:

We'll start by determining the velocity of the object. Since it is revolving in a circle of radius 8m 6 times per second, we know that:

$v = 2 \pi r \cdot 6$

Plugging in values gives us:

$v = 96 \pi$ m/s

Now we can use the standard equation for centripetal acceleration:

$a = {v}^{2} / r$
$a = {\left(96 \pi\right)}^{2} / 8$
$a = 1152 {\pi}^{2}$ m/s^2

And to finish the problem we simply use the given mass to determine the force needed to produce this acceleration:
$F = m a$
$F = 6 \cdot 1152 {\pi}^{2}$
$F = 6912 {\pi}^{2}$ Newtons