A wheel and axle is made to rotate about a horizontal axis with the help of a body of mass 6 kg attached to a string wound around the axle. The radius of the axle is 12 cm. The body falls vertically through 6 m in 12 sec starting from rest. Calculate the moment of inertia of the wheel and axle.

T=I*(d^2a/dt^2), here T - torque, T = mgR; I - moment of inertia; the expression in parantheses - second derivative of angle wrt time. This is Newtons second law for rotating objects. T and I are constant, therefore angular acceleration is also constant. What is left is to calculate angular acceleration from the height h=6m, radius R=12cm, and time t=12sec. The wheel and axle made h/(2*pi*R) revolutions with a constant angular acceleration for t seconds. This makes the angular acceleration equal to
h/(pi*R*t^2), because the initial angular speed was 0.