Before braking angular velocity was 300 rad per second. It took 10 seconds to stop. Braking was steady. How many rotations did wheel ?

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- December 30th 2006, 05:07 AMtotalnewbieAngular velocity and rotation
Before braking angular velocity was 300 rad per second. It took 10 seconds to stop. Braking was steady. How many rotations did wheel ?

- December 30th 2006, 06:08 AMtopsquark
and the wheel stopped in , so . The braking was "steady" which I will take to mean that the angular acceleration was constant. We wish to know what angle the wheel rotated through during this time period, so I'm going to set .

One way to do this is to use:

to find the then use:

to find .

The more direct way is to use:

Now we need to find out how many revolutions this is. This is a simple unit conversion: there are for every revolution. Thus:

So the answer is about 240 revolutions.

-Dan