Physics

Problem

A ceiling fan rotates at

120\,\text{rev/min}

and slows to rest with a constant angular deceleration of

0.80\,\text{rad/s}^2

in the opposite direction of its rotation. How much time elapses before the fan comes to rest? a)

12.6\,\text{s}

31.4\,\text{s}

15.7\,\text{s}

2.5\,\text{s}

Intuitive explanation

The key is recognizing that angular deceleration means the acceleration vector points opposite to the velocity vector—so you need to set up your kinematic equation with careful attention to signs. Convert the initial angular velocity to rad/s, then use $\omega_f = \omega_i + \alpha t$ with $\omega_f = 0$ to find the stopping time. The "opposite direction" phrase describes the direction of acceleration, not a change in the problem setup.

Intuitive explanation

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