A 210-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.600 rev/s in 2.00 s

The value of the constant force is .

Explanation:

Given:

Mass of the merry-go-round,

Radius of the horizontal disk,

Time required,

Angular speed,

Torque on an object is given by

where is the moment of inertia of the object, is the  angular acceleration and is the force on the disk.

The moment of inertia of the horizontal disk is given by

and the angular acceleration is given by

Substituting all these values in equation (1), we have

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