An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. (a) Find the angular acceleration in rev/s^2 and the number of revolutions made by the motor in the 4.00-s interval. (b) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part (a)?

Video transcript

Welcome back everybody. We are looking at when a engine is shut off and we're looking at the timeline of events when that engine is shut off. Now, when the engine shut off, some rotational inertia and kinetic energy is gonna keep the axles moving right. So when it's shut off we are told that the axle moving with an angular velocity of 420 revolutions per minute. Now, I'm actually gonna go ahead and convert this two revolutions per second by divided by 60 giving us an initial angular velocity of seven revolutions per second. We're also told that it slows down 260 revolutions per minute, which I'm gonna do the same thing here, divide by 60 to convert, giving us a final angular velocity of 2.67 revolutions per second. Now this all occurs in a Time period of 6.4 seconds and we are asked to find both what the angular acceleration is during this time and the number of completed revolutions during this time. So let's start with our angular acceleration here. One of our angular Kinnah Matic formulas states that our final angular velocity equal to our initial angular velocity plus our desired angular acceleration times. Time. I'm going to subtract our initial angular acceleration from both sides and divide by time, we yield that our angular acceleration equal to our final angular velocity minus our initial angular velocity. All divided by our time and plug in our values here since we know them, we have 2.67 as our final minus seven as our initial angular velocity divided by 6.4. Giving us an angular acceleration of negative 0.677 revolutions per second squared great! So now let's go ahead and find our how, find out how many revolutions were completed during this time. But we have another angular Kinnah Matic formula that states that this is equal to one half times our initial angular velocity plus our final angular velocity times our time. Don't have to do any rearranging here. Just plug in our numbers. We have one half times seven plus 2. Times 6.4 is equal to 30.9 Rev. So now we have found both our angular acceleration and our angular displacement corresponding to answer choice. E thank you all so much for watching. Hope This video helped. We will see you all in the next one.