Question

An object with a mass of `16 kg` is revolving around a point at a distance of `3 m`. If the object is making revolutions at a frequency of `13 Hz`, what is the centripetal force acting on the object?

Answer 1

I found: `320,250N`

Explanation:

Centripetal force is equal to mass time centripetal acceleration:
`F_c=m*a_c=m*v^2/r`
where:
`m=16kg=`mass;
`v=?=`linear velocity;
`r=3m=`radius.

Now:
Angular Velocity `omega` (a kind of circular velocity!) will be equal to distance divided time or:
`omega=(2pi)/T`

in this case the distance will be the circumference of `2pi` radians divided by the time or period `T` to desribe it.
But period is related to frequency `nu` as:
`nu=1/T` so we can write:
`omega=2pinu`

But we want a Linear velocity!
We simply introduce the radius into the `omega` to get:
`v=omegar=2pinur`
The centripetal force will then become:
`F_c=m(4pi^2)nu^2r^2)/r=m(4pi^2)(nu^2)r=16*(4pi^2)(13^2)*3=320,248.9N~~320,250N`