All Problems Dynamics of a solid body
Problem 1.253
A uniform cylinder of mass \(m=8.0 \mathrm{~kg}\) and radius \(R\) \(=1.3 \mathrm{~cm}\) (Fig. 1.60) starts descending at a moment \(t=0\) due to gravity. Neglecting the mass of the thread, find: (a) the tension of each thread and the angular acceleration of the cylinder; (b) the time dependence of the instantaneous power developed by the gravitational force.
1.253. (a) \(T=1 / 6 m g=13 \mathrm{~N}, \quad \beta=2 / 3 g / R=5 \cdot 10^{2} \mathrm{rad} / \mathrm{s}^{2}\) (b) \(P=2 / 3 m g^{2} t .\)