Question

A freewheel is a wheel with a hub which can rotate freely in one direction, but must rotate with a gear in the other. The gear can be thought of as "floating" in one direction and "catching" in the other. One example that most are familiar with is a bicycle wheel, though many other mechanical devices use freewheels, such as wind turbines, hydraulic turbines, grandfather clocks, and other gravity-powered objects.

A freewheel with negligible mass spokes has a mass of 1 kg and radius 2 m. A rope of length 2.3 m is attached to and coiled around its hub (radius 5 cm). At the end of the rope is a 5 kg mass. The rope-and-mass combo sits level with the center of the hub before being released.
a) If the mass is released, the rope pulls on the hub causing the wheel to spin freely. What angular velocity will the wheel have when the rope is fully unwound?
(Hints: set the hub height to h = 0, neglect the mass of the rope, assume a frictionless interaction, and assume the wheel's mass is concentrated in a ring 2 m from the rotation axis.)

b)If the mass-holding rope were instead about a hub of radius 10 cm, what would be the final angular velocity of the wheel?

Answer 1