A spinning wheel has a rotational inertia of 2 kg•m². It has an angular velocity of 6.0 rad/s. An average counterclockwise torque of 5.0 N•m is applied, and continues for 4.0 s. What is the change in angular momentum of the wheel?

Explanation:

The angular momentum of an object in rotation is given by

where

I is the moment of inertia

is the angular speed

In this problem, initially we have

is the moment of inertia of the wheel

is the initial angular speed

So the initial angular momentum is

Later, a counterclockwise torque of

is applied

So the angular acceleration of the wheel is:

in the direction opposite to the initial rotation.

As a result, the final angular velocity of the wheel will be:

where

t = 4.0 is the time interval

Solving,

which means that now the wheel is rotating in the counterclockwise direction.

Therefore, the new angular momentum of the wheel is:

So, the change in angular momentum is:

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