A small pebble breaks loose from the treadsof a tire with a radius of 34 cm. If the pebble's tangential speed is 54 m/s, what is the tire's angular speed?

158.82 rad/s

Explanation:

radius of tyre, r = 34 cm = 0.34 m

tangential speed, v = 54 m/s

Let the angular speed of the pebble is ω.

The relation between the tangential speed and the angular speed is

v = r x ω

where, r is the radius and ω be the angular speed.

54 = 0.34 x ω

ω = 158.82 rad/s

Thus, the angular speed of the pebble is 158.82 rad/s.