What is the relationship between the radius of circular motion and the centripetal force, if the mass undergoing the circular motion is kept constant?

The longer answer is a little more complicated because it appears to indicate that the centripetal force is directly proportional if the speed is measured radially in radians per second and inversely proportional if the speed is expressed linearly in meters per second. This is because the linear distance traveled around the circle's edge is also proportional to the radius; in other words, the greater the radius of the circle, the greater the force, for the same radial velocity.

The relationship between the radius of circular motion and the centripetal force, when the mass undergoing the circular motion is kept constant, is inverse square. This means that as the radius increases, the centripetal force decreases, and vice versa. The relationship is given by the formula: ( F_c = \frac{{m \cdot v^2}}{r} ), where ( F_c ) is the centripetal force, ( m ) is the mass, ( v ) is the velocity, and ( r ) is the radius.