Question

A pulley with a radius of 12 cm pulls a chain as it rotates. If the chain is moving at 4.2 cm per second, what is the angular velocity of the pulley in degrees per second?

A) 10.5 degrees/s
B) 20.8 degrees/s
C) 31.4 degrees/s
D) 42.0 degrees/s

Answer 1

The angular velocity of the pulley is 63 degrees/s.

Step-by-step explanation:

The angular velocity of the pulley can be calculated using the formula:

angular velocity = linear velocity / radius

Given that the linear velocity of the chain is 4.2 cm/s and the radius of the pulley is 12 cm, we can substitute the values into the formula:

angular velocity = 4.2 cm/s / 12 cm = 0.35 rad/s

To convert the angular velocity from radians per second to degrees per second, we use the conversion factor:

1 rad/s = 180 degrees/s

Therefore, the angular velocity of the pulley is:

0.35 rad/s * 180 degrees/s = 63 degrees/s