alleryStart learning →A wheel turning at 26.2 rad/s is braked, giving an angular acceleration of -87.3 rad/s^2. How long does it take to stop?
A3.33 s
B2.29 s
C0.113 s
D0.300 s
Answer & Solution
Correct answer: D. 0.300 s
1. Rearrange alpha = delta omega / delta t to give delta t = delta omega / alpha.
2. The angular velocity falls from 26.2 rad/s to zero, so delta omega = -26.2 rad/s.
3. The braking angular acceleration is alpha = -87.3 rad/s^2.
4. So delta t = (-26.2 rad/s) / (-87.3 rad/s^2) = 0.300 s.
5. Both quantities are negative, so the time comes out positive, as any real duration must.
6. Dividing the other way round gives 3.33 s, which is the reciprocal and carries wrong units.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.1 Angular Acceleration_
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