All Problems

Dynamics of a solid body

Problem 1.246

In the arrangement shown in Fig. 1.56 the mass of the uniform solid cylinder of radius \(R\) is equal to \(m\) and the masses of two bodies are equal to \(m_{1}\) and \(m_{2} .\) The thread slipping and the friction in the axle of the cylinder are supposed to be absent. Find the angular acceleration of the cylinder and the ratio of tensions \(T_{1} / T_{2}\) of the vertical sections of the thread in the process of motion.

Reveal Answer
β=∣m2−m1∣g(m1+m2+m/2)R,T1T2=m1(m+4m2)m2(m+4m1)\beta=\frac{\left|m_{2}-m_{1}\right| g}{\left(m_{1}+m_{2}+m / 2\right) R}, \quad \frac{T_{1}}{T_{2}}=\frac{m_{1}\left(m+4 m_{2}\right)}{m_{2}\left(m+4 m_{1}\right)}
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