Question

A truck with 0.300 m radius tires travels at 28.0 m/s.

a) What is the angular velocity of the rotating tires in radians per second?
b) What is this in revolutions per minute?

Answer 1

Angular velocity = 93.33 radians/second

Revolutions per minute = 1,782.51 revolutions per minute

Explanation:

The relation between angular velocity, ω and linear velocity, v is given by the equation

`\omega = (v)/(r)`

where ω is in radians per second

v = m/s

and r is the radius (m) of the circular motion, in this case, the radius of the tire

Given v = 28 m/s and r = 0.300 m

we get

`\omega = (28 \;m/s)/(0.3\;m) = 93.33 \;radians/second`

Since 2π radians make a full revolution, 93.33 radians/sec = 93.33 ÷ 2π = 29.708 revolutions per second

To get the revolutions per minute, multiply this by 60 since there are 60 seconds to a minute:

29.708 x 60 = 1,782.51 revolutions per minute