00:01
So the problem tells us that a wheel starts spinning at 500 revolutions per minute, and 120 seconds later, it's spinning at 1 ,500 revolutions per minute.
00:11
And the question asks us to find what the angular acceleration is equal to, as well as what the angular displacement is of the wheel.
00:21
So first, let's convert these revolution per minute units into rates, per second so we can get the angular velocity.
00:33
So to do this, we can take our 500 revolutions per minute and use dimensional analysis to get radiance per second.
00:45
So we have 500 revolutions per one minute.
00:50
And in one revolution, we have two pi radians.
00:57
And in one minute, we have 60 seconds.
01:02
And so if we put this into a calculator, we'll see that 500 revolutions per minute is approximately equal to 52 .36 radians per second.
01:22
So now that we have this, we can figure out what the final velocity is.
01:29
And it's just the exact same dimensional analysis.
01:32
So we have 1 ,500 revolutions per minute, and in one revolution, we have 2 pi radians, and in one minute we have 60 seconds.
01:54
And so putting this into a calculator, we'll see that the final angular velocity is equal to 157 .08 radians per second...