Question

An object with a mass of `7 kg` is revolving around a point at a distance of `8 m`. If the object is making revolutions at a frequency of `4 Hz`, what is the centripetal force acting on the object?

Answer 1

Data:-

Mass`=m=7kg`
Distance`=r=8m`
Frequency`=f=4Hz`
Centripetal Force`=F=??`

Sol:-

We know that:

The centripetal acceleration `a` is given by
`F=(mv^2)/r................(i)`

Where `F` is the centripetal force, `m` is the mass, `v` is the tangential or linear velocity and `r` is the distance from center.

Also we know that `v=romega`

Where `omega` is the angular velocity.

Put `v=romega` in `(i)`

`implies F=(m(romega)^2)/r implies F =mromega^2...........(ii)`

The relation between angular velocity and frequency is

`omega=2pif`

Put `omega=2pif` in `(ii)`

`implies F=mr(2pif)^2`
`implies F=4pi^2rmf^2`

Now, we are given with all the values

`implies F=4(3.14)^2*8*7*(4)^2=4*9.8596*8*16=35336.8064`

`implies F=35336.8064N`