Consider a collar with mass m that is free to slide with no friction along a rotating arm,...

Consider a collar with mass m that is free to slide with no friction along a rotating arm, which has negligible mass. The system is initially rotating with an angular velocity ω0 while the collar is kept a distance r0 away from the z axis. At some point, the restraint keeping the collar in place is removed so that the collar is allowed to slide.

Figure P3.79

Compute the moment Mz that you would need to apply to the arm, as a function of r, to keep the arm rotating at a constant angular velocity ω0. In addition, determine the radial speed as well as the total speed with which the collar would reach the end of the arm with this moment applied. Hint: The moment Mz applied to the arm of negligible mass is equivalent to a force Mz/r applied to the collar in the plane of motion and perpendicular to the arm.