alleryStart learning →A point goes once round a circle in a time T. What is its angular velocity, in radians per unit time?
A2 pi T radians per unit time
BT / 2 pi radians per unit time
C2 pi / T radians per unit time
D1 / T radians per unit time
Answer & Solution
Correct answer: C. 2 pi / T radians per unit time
1. Angular velocity is angle swept divided by time taken.
2. One full revolution sweeps 2 pi radians, and it takes a time T.
3. So omega = 2 pi / T radians per unit time.
4. Writing 1 / T gives the frequency in cycles per unit time, which is smaller by the factor 2 pi.
5. Multiplying by T instead of dividing would make a slow rotation have a large angular velocity, which is backwards.
_Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section 16.6 Uniform Circular Motion and Simple Harmonic Motion_
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