# [SOLVED] Trigonometry test question

• Jan 31st 2009, 09:06 PM
uniquelymindy
[SOLVED] Trigonometry test question
There are three rollers under a conveyor belt, and each roller has a radius of 8 centimeters. The rollers turn at a rate of 2 revolutions per second. What is the linear velocity of the conveyor belt? (the centimeters has to be converted into meters.)

the linear velocity of any point rotating about a fixed axis with an angular velocity of $\omega$ is $r \omega$ where r is the distance between the point and axis.
The conveyor belt must be moving at the same speed as the rollers (at the point of contact ) therefore $v = r \omega$ where r is the radius of the rollers i.e. 0.08 m. remember $\omega$ is the rate of change of the angle . the rollers turn 2 revolutions in a second .therefore they turn at the rate of $4 \pi$ per second .
impling $v = 0.08 \times 4\pi$.