A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 $\mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle does the pulley turn in 5.26 s?
A) 19.3 rad
B) 22.6 rad
C) 113 rad
D) 160 rad
E) 42.6 rad

Question

A pulley has an initial angular speed of  12.5 rad/s and a constant angular acceleration of  3.41  $\mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle does the pulley turn in  5.26 s?
A)  19.3 rad
B)  22.6 rad
C)  113 rad
D)  160 rad
E)  42.6 rad

Quizplus · Accepted Answer

The angle through which the pulley turns can be found using the formula $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\theta$ is the angle in radians, $\omega_0$ is the initial angular speed, $\alpha$ is the angular acceleration, and $t$ is the time. Substituting the given values: $\theta = 12.5 \times 5.26 + \frac{1}{2} \times 3.41 \times (5.26)^2 = 113$ rad.

A Pulley Has an Initial Angular Speed of 12 rad/s2\mathrm { rad } / \mathrm { s } ^ { 2 }rad/s2

A Pulley Has an Initial Angular Speed of 12 $\mathrm { rad } / \mathrm { s } ^ { 2 }$