Question

A grinding wheel with a moment of inertia of 2.0 kg•mº is initially at rest. What angular momentum will the wheel have 10.0 s after a 2.5 N·m torque is applied to it?

a. 25 kg•m/s
b. 4.0 kg•m/s
c. 7.5 kg•m/s
d. 0.25 kg•m/s

Answer 1

25 kg m^2/s

Step-by-step explanation:

The angular acceleration due to the application of torque to the grinding wheel is:

`\tau=I\alpha \rightarrow \alpha=(2.5)/(2)=1.25` (in radian per square second)

So, by the basic equation of the angular acceleration, we can get the angular velocity at t = 10 s as follows:

`\omega=\omega_(o)+\alpha t \rightarrow \omega =0+(1.25)(10) =12.5` rad/s.

So, the angular momentum at t = 10 s:

`L=I\omega=(2)(12.5) = 25` kg m^2/s