Question

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. as the string is pulled, the pulley rotates without any slipping of the string. what is the angular speed of the pulley when the string is moving at 5.0 m/s?

Answer 1

The angular speed can be solve using the formula:
w = v / r
where w is the angular speed
v is the linear velocity
r is the radius of the object

w = ( 5 m / s ) / ( 5 cm ) ( 1 m / 100 cm )
w = 100 per second

Answer 2

Answer:

Angular speed of the pulley = 100 rad/s

Explanation:

Linear speed = Angular speed x Radius

    v = ωr

Given that the string is moving at 5.0 m/s

That is v = 5 m/s

The string is wound tightly around a fixed pulley having a radius of 5.0 cm,

           r = 5 cm = 0.05 m

Linear speed = Angular speed x Radius

5 = ω x 0.05

ω = 100 rad/s

Angular speed of the pulley = 100 rad/s