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Math Help - Angular velocity and rotation

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    Angular 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 ?
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    Quote Originally Posted by totalnewbie View Post
    Before braking angular velocity was 300 rad per second. It took 10 seconds to stop. Braking was steady. How many rotations did wheel ?
    \omega_0 = 300 \, rad/s and the wheel stopped in t = 10 \, s, so \omega = 0 \, rad/s. The braking was "steady" which I will take to mean that the angular acceleration \alpha was constant. We wish to know what angle the wheel rotated through during this time period, so I'm going to set \theta _0 = 0 \, rad.

    One way to do this is to use:
    \omega = \omega _0 + \alpha t
    to find the \alpha then use:
    \theta = \theta _0 + \omega _0 t + \frac{1}{2} \alpha t^2
    to find \theta.

    The more direct way is to use:
    \theta = \theta _0 + \frac{1}{2}( \omega _0 + \omega )t

    \theta = \frac{1}{2} \omega _0 t

    \theta = \frac{1}{2} (300 \, rad/s) (10 \,s ) = 1500 \, rad

    Now we need to find out how many revolutions this is. This is a simple unit conversion: there are 2 \pi \, rad for every revolution. Thus:
    \frac{1500 \, rad}{1} \cdot \frac{1 rev}{2 \pi \, rad} \approx 238.732 rev

    So the answer is about 240 revolutions.

    -Dan
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