A frictionless hoop of radius R is made to rotate at constant angular speed w around a diameter. A bead on the hoop starts on this diame- ter and is then given a tiny kick. Let N be the total force that the hoop applies to the bead, and let N₁ be the component of N that is perpendic- ular to the plane of the hoop. Where is N₁ maximum? What is the mag- nitude of N as a function of position? (Ignore gravity in this problem.

A frictionless hoop of radius R is made to rotate at constant angular speed w around a diameter. A bead on the hoop starts on this diame- ter and is then given a tiny kick. Let N be the total force that the hoop applies to the bead, and let N₁ be the component of N that is perpendic- ular to the plane of the hoop. Where is N₁ maximum? What is the mag- nitude of N as a function of position? (Ignore gravity in this problem.