alleryStart learning →A reel turning at 220 rad/s is braked with an angular acceleration of -300 rad/s^2. How long does it take to come to rest?
A0.733 s
B1.36 s
C0.367 s
D73.3 s
Answer & Solution
Correct answer: A. 0.733 s
1. Use omega = omega_0 + alpha t and solve for t, giving t = (omega - omega_0) / alpha.
2. The final angular velocity is zero and the initial one is 220 rad/s.
3. Substituting, t = (0 - 220 rad/s) / (-300 rad/s^2).
4. Both numerator and denominator are negative, so t = 0.733 s.
5. Inverting the fraction gives 1.36 s, which has units of s squared per rad and cannot be a time.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.2 Kinematics of Rotational Motion_
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