Express the angular speed in radians per second.
-A gear with a radius of 32 centimeters is turning at $\frac { \pi } { 3 }$ radians per sec. What is the linear speed at a point on the outer edge of the gear?
A) $\frac { 32 \pi } { 3 }$ centimeters per second
B) $\frac { 3 \pi } { 32 }$ centimeters per second
C) $96 \pi$ centimeters per second
D) $\frac { \pi } { 96 }$ centimeters per second

Question

Quizplus · Accepted Answer

The linear speed $v$ at the edge of a rotating object is given by $v = r\omega$, where $r$ is the radius and $\omega$ is the angular speed. Here, $r = 32$ cm and $\omega = \frac{\pi}{3}$ radians per second, so $v = 32 \cdot \frac{\pi}{3} = \frac{32\pi}{3}$ cm/s.

Express the Angular Speed in Radians Per Second π3\frac { \pi } { 3 }3π​

Express the Angular Speed in Radians Per Second $\frac { \pi } { 3 }$