A wheel rotates without friction about a stationary horizontal axis at the center of the wheel. A constant tangential force equal to 80.0 N is applied to the rim of the wheel. The wheel has radius 0.120 m. Starting from rest, the wheel has an angular speed of 12.0 rev/s after 2.00 s. What is the moment of inertia of the wheel?

Solution 15E Step 1: Data given Tangential force F tan= 80.0 N Radius R = 0.120 m Final velocity v f 12.0 rev /s v f 12.0 rev/s × (2/1 rev) = 75.39 rad /s Time taken t = 2.0 s We shall find the angular acceleration of the wheel This is given by a = v ft Substituting values we get a = 75.39 rad /s/2.0 s a = 37.69 rad /s 2 Step 2 : We shall find the torque of the wheel It is given by = F × r Substituting values we get = 80.0 N × 0.120 m = 9.6 Nm