Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same

Question

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. Which of the two will acquire a greater angular speed after a given time?

Professor PC Thomas Classes · Answer

Angular acceleration is given by $\alpha = \frac{	au}{I}$. Since the torque $	au$ is the same, the body with the smaller moment of inertia $I$ will have a greater angular acceleration and thus a greater angular speed. The moment of inertia of a solid sphere ($\frac{2}{5}MR^2$) is less than that of a hollow cylinder ($MR^2$). Therefore, the solid sphere acquires a greater angular speed.