(II) A cooling fan is turned off when it is running at 780 rev...

Question

(II) A cooling fan is turned off when it is running at 780 rev/min . It turns 1250 revolutions before it comes to a stop.

(b) How long did it take the fan to come to a complete stop?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A helicopter landed on a helipad soon after the engine was switched off when the rotor blades were rotating at 730 revolutions per minute. After completing 1120 revolutions, the rotor blades came to a stop, determine the time the rotor blades took to stop after the engine was shut down. So that's our end goal. Ultimately, we're trying to figure out how long it took for the blades on the helicopter to stop spinning, to stop rotating once the engine was shut down. Awesome. So that's the final answer we're ultimately trying to figure out is how much time it took for this to happen. We're also given some multiple choice answers. They're all in units of seconds. Let's read them off to see what our final answer might be. A is 0.77 B is 3.1 C is 46 and D is 184. OK. So first off, let us write down all of our known and unknown variables. We know that the initial angular velocity, which we're gonna denote as omega zero is equal to 730 revolutions per minute. We also know that the final angular velocity which we're just gonna call Omega is equal to zero revolutions per minute because it's not gonna be moving anymore. It's gonna go back to rest, back to its equilibrium position. And we also know that the angle made by the rotor blades is the, is equal to 1120 revolutions. And we know that the time taken actually, I, we say that we know, but we do not know, we do not know what tea is. So off to the side here, we do not know what T is. We're trying to figure out the time that it takes for these blades to stop moving. So T our final answer, we do not know what this answer is. So now we need to recall that theta is equal to omega zero, my omega zero plus omega divided by two multiplied by T. So now as you can see if you haven't figured it out already, we need to rearrange this equation to isolate and solve for T. And that will help us solve for our final answer. So when we use some algebra to rearrange this equation to isolate and solve for T, we will get that T is equal to two multiplied by theta, all divided by omega zero plus Omega, which is equal to. So now we can plug in all of our known variables to help us solve the numerical value of T. We also need to quickly note here that we have a bit of a predicament here because right now our original units are in revolutions per minute, but we want our final answer in seconds. So we're gonna have to convert minutes to seconds. OK. Which we'll do in a second. So don't panic. But we ha that's what we're gonna be doing. That's a little brief, little rundown of what's gonna happen here. So we need to take two multiplied by 1120 revolutions. And we need to divide this by 730 revolutions per minute plus zero revolutions per minute. And the do our conversion. We need to recall some dimensional analysis and we can remember hopefully that there is 60 seconds in one minute. So when we plug that into our calculator, we will find that our value of T is equal to 184 seconds when we round to the nearest whole number. And that's it we solve for this problem. Hooray. We did it. Who? So just to quickly show right here, we know that one minute will cancel out with our minute units leaving us with just seconds, which is perfect. And then our revolution units will cancel out, leaving us just with units of seconds, which is exactly what we want and don't forget that there's a parent, don't forget your parentheses, make sure we keep everything consistent and that's it we solve for this problem. So looking at our multiple choice answers, the correct answer has to be the letter D which is 184 seconds and that's it for this video. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

(II) A cooling fan is turned off when it is running at 780 rev/min . It turns 1250 revolutions before it comes to a stop.
(b) How long did it take the fan to come to a complete stop?

Key Concepts

Angular Velocity

Angular Deceleration

Kinematic Equations for Rotational Motion

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