Question

A wheel of radius 10 cm can rotate freely about its centre as shown in figure. A stirng is wrapped over its rim and is ulle dby a force of 5.0 N. It is found that the torque roduces an angular acceleration 2.0 `rad/s^2` in the wheel. Calculate the moment of inertia of the wheel.

Answer 1

The forces acting on the wheel are i. W due to gravity ii N due to the support at the cnetre and iii F due to tension. The torque of W and N are separately zero and that of F is F.r. The net torque is
`Gamma=(5.0N).(10cm)=0.50N.m.`
The moment of inertia is
`I =Gamma/a=(0.50N-m)/(2rads62)=0.25kg-m^2`