The flywheel of an engine has moment of inertia 1.60 kg/m^2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8.00 s, starting from rest?

Video transcript

Welcome back everybody. We are making observations about a solid disk and we are told that its moment of inertia is 5.4 kg meters squared relative to its axis of rotation. Now we are told that We need that moment of inertia in order to spin at an angular velocity of 850 rpm minute. We're told also that the disc initially starts out at rest and that let's see here. We need to determine what the torque is after 4.5 seconds of rotation. So in order to calculate our torque, we are going to need this formula here that our torque is equal to the moment of inertia times our angular acceleration. We have our moment of inertia right here, but we need to figure out what this term is. So we are going to use Kinnah Matic formulas for that. We have that our final angular velocity is equal to our initial angular velocity plus our angular acceleration times time. I subtract this value, this initial velocity from both sides and then divide by T on both sides. You're going to see that these terms cancel out and we get that our angular acceleration is equal to our final angular velocity minus our initial angular velocity all over our time. Now, before we can start plugging in terms however, we need to make sure everything's in the right units. And I'm looking up here at this guy. We cannot have it in revolutions per minute. We must have it in radiance per second. So let me go ahead and convert it here Per one revolution. We have two pi radiance and per one minute we have 60 seconds as you'll see. These units will cancel out on top and bottom. And when you multiply straight across we get that our final angular velocity was 89 radiance per second. Right now we have everything in the right units. Let's go ahead and find our angular acceleration. We have that our angular acceleration is equal to 89 0, all divided by 4.5 seconds. And when you plug this into your calculator, we get an angular acceleration of 19.8 radiance per second squared great! Now that we have that we are good to go on finding our torque once again as a reminder, it is our moment of inertia times are angular acceleration. So let's plug that in. We have that are i is equal to 5.4. We just found our angular acceleration to be 19.8. And when we multiply this straight across, we get that. Our final answer is one oh seven Newton meters corresponding to our answer choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one