Physics

Physics

Problem

A ceiling fan starts from rest and has a constant angular acceleration of 4 rad s−24\,\text{rad s}^{-2}. Through what angle does it rotate in the first 5 s5\,\text{s}? a) 20 rad20\,\text{rad} b) 50 rad50\,\text{rad} c) 100 rad100\,\text{rad} d) 25 rad25\,\text{rad}
Intuitive explanation

This is a rotational kinematics problem—the angular equivalent of finding distance traveled under constant acceleration. Since you know the initial angular velocity (zero), angular acceleration, and time, you can use the rotational version of the kinematic equation s=ut+12at2s = ut + \frac{1}{2}at^2, but with angular quantities: θ=ω0t+12αt2\theta = \omega_0 t + \frac{1}{2}\alpha t^2. Just plug in your values and solve.

Intuitive explanation

This is a rotational kinematics problem—the angular equivalent of finding distance traveled under constant acceleration. Since you know the initial angular velocity (zero), angular acceleration, and time, you can use the rotational version of the kinematic equation s=ut+12at2s = ut + \frac{1}{2}at^2, but with angular quantities: θ=ω0t+12αt2\theta = \omega_0 t + \frac{1}{2}\alpha t^2. Just plug in your values and solve.

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