A disk rotates about its central axis starting from rest and...

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15 rev/s. Calculate (a) the angular acceleration, (b) the time required to complete the 60 revolutions, (c) the time required to reach the 10 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 10 rev/s angular speed.

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00:01 Okay, let's see what we got here.

00:05 At one time, it is rotating 10 revolutions per second.

00:12 So at some time, it's rotating at 10 revolutions per second.

00:26 So i'm going to say that it's at omega -0.

00:30 60 revolutions later, now it's rotating at 15 per second.

00:52 What's the angular acceleration? well, the angular acceleration is going to be the change in angular velocity, which would be the 15 minus 10, so that's going to be five revolutions per second, over, uh -oh, the amount of time.

01:15 E.

01:16 Okay.

01:19 Omega final squared equals omega initial squared equals omega initial squared.

01:24 Minus or plus 2a to alpha delta theta.

01:39 So 15 squared equals 10 squared plus 2 alpha times 60.

01:50 So 15 squared is 225.

01:54 10 squared is 100.

01:56 225 minus 100 is 125 divided by 120 and that's going to be alpha putting that in a calculator 1 .04 but we only have two significant digits so i'm going to write alpha here anyway but it's really only 1 .0 revolutions per second squared b how much time does it take to complete the 60 revolutions? okay.

03:06 Well, we know alpha, and so i can just use the equation that i already created up here.

03:11 I didn't actually need until now.

03:15 T is going to be 5 over alpha, because it's 5 revolutions per second divided by alpha...

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