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