alleryStart learning →Which rotational equation links angular velocity to angle turned without involving time?
Aomega^2 = omega_0^2 + alpha theta
Bomega^2 = omega_0^2 - 2 alpha theta
Comega^2 = omega_0^2 + 2 alpha t
Domega^2 = omega_0^2 + 2 alpha theta
Answer & Solution
Correct answer: D. omega^2 = omega_0^2 + 2 alpha theta
1. The straight-line counterpart is v squared = v_0 squared + 2 a x.
2. Replacing v by omega, a by alpha and x by theta gives omega^2 = omega_0^2 + 2 alpha theta.
3. Time does not appear, which is what makes this form useful when t is unknown.
4. The version ending in t mixes an angle equation with a time variable and is dimensionally wrong.
_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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