Applications of Circular Motion

Having established that some real force must supply the centripetal requirement $\dfrac{mv^2}{r}$, we now apply this to several classic scenarios. In each, the strategy is the same: draw a free-body diagram, identify the real forces, and resolve them so that the net inward component equals $\dfrac{mv^2}{r}$. The differences lie only in which forces are present and how they are oriented.

Consider first a car turning on a flat road. The only horizontal force available to bend the car's path is the friction between the tires and the road surface, acting sideways toward the center of the turn. Setting friction equal to the centripetal requirement gives $f = \dfrac{mv^2}{r}$. The maximum available static friction is $f_{max} = \mu m g$, where $\mu$ is the coefficient of static friction. The fas