A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of $0.100 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ and the wheel slows uniformly to a stop in 160 s, what is the magnitude of the retarding torque?
A) $1,33 \mathrm {~N} \cdot \mathrm { m }$
B) $1.67 \mathrm {~N} \cdot \mathrm { m }$
C) $0.00750 \mathrm {~N} \cdot \mathrm { m }$
D) $0.0787 \mathrm {~N} \cdot \mathrm { m }$
E) $1.00 \mathrm {~N} \cdot \mathrm { m }$

Question

A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of  12.0 rad/s  and then allows it to coast to a stop. If the wheel has a moment of inertia of $0.100 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ and the wheel slows uniformly to a stop in  160 s, what is the magnitude of the retarding torque?
A) $1,33 \mathrm {~N} \cdot \mathrm { m }$
B) $1.67 \mathrm {~N} \cdot \mathrm { m }$
C) $0.00750 \mathrm {~N} \cdot \mathrm { m }$
D) $0.0787 \mathrm {~N} \cdot \mathrm { m }$
E) $1.00 \mathrm {~N} \cdot \mathrm { m }$

Quizplus · Accepted Answer

The magnitude of the retarding torque can be found using the formula $\tau = I \alpha$, where $I$ is the moment of inertia and $\alpha$ is the angular deceleration. First, find $\alpha = \Delta \omega / \Delta t = -12.0 \, \text{rad/s} / 160 \, \text{s} = -0.075 \, \text{rad/s}^2$. Then, $\tau = 0.100 \, \text{kg} \cdot \text{m}^2 \times -0.075 \, \text{rad/s}^2 = -0.0075 \, \text{N} \cdot \text{m}$, taking the magnitude gives $0.0075 \, \text{N} \cdot \text{m}$.

A Mechanic Is Examining the Wheel of a Bicycle to Adjust