A grinding wheel has a mass of 250 kg and moment of inertia of 500 kg m². A torque of 100 N•m is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds? A) 650 kg m²/s B) 500 kg m²/s C) 450 kg m²/s D) 300 kg m²/s E) 250 kg m²/s

Question

Quizplus · Accepted Answer

First, we need to use the torque and moment of inertia to find the angular acceleration:

$	au = I\alpha$

$100	ext{ N}\cdot	ext{m} = 500	ext{ kg m}^2\cdot\alpha$

$\alpha = 0.2	ext{ rad/s}^2$

Then, we can use the angular acceleration and time to find the change in angular velocity:

$\alpha = \frac{\Delta\omega}{\Delta t}$

$\Delta\omega = \alpha\Delta t$

$\Delta\omega = 0.2	ext{ rad/s}^2\cdot5	ext{ s} = 	extbf{1 rad/s}$

Finally, we can use the moment of inertia and final angular velocity to find the angular momentum:

$L = I\omega$

$L = 500	ext{ kg m}^2\cdot1	ext{ rad/s} = \boxed{	extbf{500 kg m}^2	extbf{/s}}$

A Grinding Wheel Has a Mass of 250 Kg and Moment