Question

A wheel rotates at 20.0 rpm. a. Find the angular velocity in radians/second; If the radius is 3.0 meters,b. Find the linear speed of a point on the edge of the wheel.

Answer 1

ANSWERS

a. 2.09 rad/s

b. 6.27 m/s

EXPLANATION

a. The wheel gives 20 turns in 1 minute. Since the wheel is a circle, 1 turn is equivalent to 2π radians. Also, 1 minute has 60 seconds,

$20rpm=20\frac{rev}{\min}\cdot\frac{1\min}{60s}\cdot\frac{2\pi rad}{1rev}\approx2.09rad/s$

Hence, the angular velocity is 2.09 rad/s

b. What we have to find in this part is the tangential speed, which is related to the angular velocity and re radius of rotation by the equation,

$v=r\cdot\omega$

The radius of the wheel is 3m, so the tangential speed is,

$v=3m\cdot2.09rad/s=6.27m/s$