All Problems Dynamics of a solid body
Problem 1.260
A uniform solid cylinder \(A\) of mass \(m_{1}\) can freely rotate about a horizontal axis fixed to a mount \(B\) of mass \(m_{2}\) (Fig. 1.66). A constant horizontal force \(F\) is applied to the end \(K\) of a light thread tightly wound on the cylinder. The friction between the mount and the supporting horizontal plane is assumed to be absent. Find: (a) the acceleration of the point \(K\); (b) the kinetic. energy of this system \(t\) seconds after the beginning of motion.
(a) \(w=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)}\) (b) \(T=\frac{F^{2} t^{2}\left(3 m_{1}+2 m_{2}\right)}{2 m_{1}\left(m_{1}+m_{2}\right)}\)