The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The 120-lb rotor, which has a centroidal radius of gyration of 9 in., then coasts to rest. Knowing that kinetic friction results in a couple of magnitude 2.5 lb·ft exerted on the rotor, determine the number of revolutions that the rotor executes before coming to rest.

Consider a rigid body initially at rest and subjected to an impulsive force F contained in the plane of the body. We define the center of percussion P as the point of intersection of the line of action of F with the perpendicular drawn from G(a) Show that the instantaneous center of rotation C of the body is located on line GP at a distance GC = k2/GP on the opposite side of G. (b)  Show that if the center of percussion were located at C, the instantaneous center of rotation would be located at P.

Please display all work

A disk with radius R and mass m begins from rest and then moves without slipping while being pulled horizontall by a force P acting at its center axle. Show that the velocity of the wheel after T seconds is v= 2PT/3m. (Hint: use both linear and angular-impulse principles.) m REG P ¹The radius of gyration has units of length and is related to the inertia by k = IG/m. It corresponds to the distance at which a mass equivalent to the mass of the rigid body would produce the same inertia as the actual rigid body. Recall that the inertia of a particle of mass m at a distance r from an axis of ortation is mr². Rather that using r the convention is to define the radus of gyration with the symbol k.