The wheel on a vehicle has a rotational inertia of 2.0 kg*m^2. at the instant the wheel has a counterclockwise 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?

We can use the equivalent of 

for rotational motions:

where
is the torque applied to the object
is the variation of angular momentum
is the time interval

In our problem,  and , so keeping in mind that the torque is in the same direction of the initial angular speed of the object (therefore, the variation of angular momentum should be positive), we have

The change in angular momentum of the wheel is equal to .

Given the following data:

Rotational inertia = 2.0 Angular velocity = 6.0 rad/sTorque = 5.0 NmTime = 4 seconds

To calculate the change in angular momentum of the wheel:

Mathematically, the change in angular momentum is given by this formula:

Where:

is the change in angular momentum. is the torque.t is the time measured in seconds.

Substituting the given parameters into the formula, we have;

Read more on angular momentum here: link

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.

This is the answer of your question