alleryStart learning →Which rotational equation gives the angle turned in time t under constant angular acceleration?
Atheta = omega_0 t + alpha t
Btheta = omega_0 t + 0.5 alpha t^2
Ctheta = omega_0 t + 2 alpha t^2
Dtheta = omega_0 t - 0.5 alpha t
Answer & Solution
Correct answer: B. theta = omega_0 t + 0.5 alpha t^2
1. The straight-line counterpart is x = v_0 t + one half a t squared.
2. Rotational kinematics is exactly analogous, with theta for x, omega for v and alpha for a.
3. So theta = omega_0 t + 0.5 alpha t^2 for constant alpha.
4. The factor of one half comes from averaging the angular velocity over the interval.
5. A factor of 2 in place of 0.5 would overstate the angle turned by a factor of four.
_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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