alleryStart learning →A force perpendicular to r acts on a point mass m at distance r from a pivot. Which relation follows from Newton's second law?
Atau = m r alpha
Btau = m alpha / r
Ctau = m r^2 alpha
Dtau = m r^2 alpha^2
Answer & Solution
Correct answer: C. tau = m r^2 alpha
1. Newton's second law for the point mass gives F = m a.
2. For circular motion a = r alpha, so F = m r alpha.
3. Because F is perpendicular to r, the torque is simply tau = r F.
4. Multiplying both sides by r gives r F = m r^2 alpha, that is tau = m r^2 alpha.
5. The quantity m r squared plays the role of mass and is the moment of inertia of the point mass.
6. Squaring alpha would break the direct proportionality between torque and angular acceleration.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.3 Dynamics of Rotational Motion: Rotational Inertia_
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