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

1 Answer
Nathan L.
Jun 28, 2017

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.

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