alleryStart learning →What does the net work done by a torque on a rotating body equal?
AThe final rotational kinetic energy alone
BThe change in rotational kinetic energy
CThe sum of both rotational kinetic energies
DThe initial rotational kinetic energy alone
Answer & Solution
Correct answer: B. The change in rotational kinetic energy
1. Substituting net tau = I alpha into net W = (net tau) theta gives net W = I alpha theta.
2. The kinematic relation omega squared = omega_0 squared + 2 alpha theta gives alpha theta = (omega squared minus omega_0 squared) / 2.
3. So net W = one half I omega squared minus one half I omega_0 squared.
4. That is the change in rotational kinetic energy, the work-energy theorem for rotation.
5. Equating the work to the final energy alone would only be right if the body started from rest.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.4 Rotational Kinetic Energy: Work and Energy Revisited_
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