Question

What is the relationship between the force needed to maintain circular motion and the squared velocity of an object? Please help

Answer 1

They are directly proportional...

Explanation:

In uniform circular motion (constant speed around a circlular path), the centripetal acceleration `a_"rad"` (acceleration directed toward center of circle) is equal to the square of the speed divided by the radius of the circle:

`a_"rad" = (v^2)/r`

And the magnitude of the centripetal force `F_r` is

`F_r = ma_"rad"`

So, combining the two equations, we can get a relationship between the force and the square velocity:

`F_r = (mv^2)/r`

And from this relationship, the constant force is directly proportional to the square of the speed.