alleryStart learning →How is tangential acceleration related to angular acceleration for a point at radius r?
Aa_t = r times alpha
Ba_t = alpha over r
Ca_t = r over alpha
Da_t = r times alpha squared
Answer & Solution
Correct answer: A. a_t = r times alpha
1. Start from a_t = delta v / delta t and substitute v = r omega.
2. The radius is constant in circular motion, so delta(r omega) = r delta omega.
3. That gives a_t = r delta omega / delta t, and delta omega / delta t is alpha.
4. Hence a_t = r alpha, so the two accelerations are directly proportional.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.1 Angular Acceleration_
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