A ceiling fan is initially rotating counterclockwise at an angular speed of

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

20\,\text{rad/s}

. At

t=0

the fan’s motor increases the torque so that the fan experiences a constant angular acceleration of

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

for

4.0\,\text{s}

. Immediately after this interval the motor is switched off, and friction produces a constant angular deceleration of

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

(opposite the rotation direction) until the blades come to rest. (a) Determine the time required for the fan to come to rest after the motor is switched off. (b) Calculate the total angular displacement of the fan blades from

t=0

until they stop. (c) Compute the average angular acceleration for the entire motion from

t=0

until the fan stops, and explain the physical significance of its sign.

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