A uniform disc of mass 16 kg and radius 0.40 m turns on a fixed axle through its centre…

For rotation about a fixed axis: $\tau = I\alpha$, kinetic energy $\tfrac12 I\omega^2$, work $\tau\theta$, power $\tau\omega$. A rope on a wheel links the two motions: $a = \alpha R$.

Moment of inertia: $I = \sum m_ir_i^2$. Ring $MR^2$; disc $\tfrac12 MR^2$; rod $\tfrac{1}{12}ML^2$ about its middle; solid sphere $\tfrac25 MR^2$. Parallel axes: $I = I_{cm} + Md^2$. Flat bodies: $I_z = I_x + I_y$.