Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 22 N is applied tangentially to a sprocket of radius 6 cm for 6 s, what angular speed does the wheel achieve, assuming it rolls without slipping?

The angular speed after 6s  is .

Explanation:

The equation

relates the moment of inertia of a rigid body, and its angular acceleration , with the force applied at a distance from the axis of rotation.

In our case, the force applied is , at a distance , to a ring with the moment of inertia of ; therefore, the angular acceleration is

Therefore, the angular speed which is

after 6 seconds is