A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 16 rpm in 11.0 s . Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Part A Calculate the torque required to produce the acceleration, neglecting frictional torque. Part B What force is required at the edge?

(a)

Step 1:

Mass of the merry go round is 560 kg.

Mass of each children is 25 kg.

Radius of the disk is 2.5 m.

The initial angular speed is 0 rad/sec.

The final angular speed is .

Find torque.

Torque , where I is the total moment of inertia and a is the acceleration.

Find the acceleration.

Step 2:

Find total moment of inertia.

Total moment of inertia .

  is the moment of inertia of the merry-go-round and is moment of inertia of two childrens

Moment of inertia of a uniform cylinder is .

Moment of inertia of a uniform cylinder is 1750 kg-m².

Moment of inertia of two childrens is .

Moment of inertia of two childrens is 156.25 kg-m².

Total moment of inertia .

Total moment of inertia is 1906.25 kg-m².

Torque .

Torque required to produce the acceleration 289.4 Nm.

Solution:

Torque required to produce the acceleration 289.4 Nm.

(b)

From part (a):

Torque required to produce the acceleration 289.4 Nm.

Radius of the disk is 2.5 m.

Force is applied at a 90^o angle to the radius, the torque is , where F is the force and r is the radius.

Force required is 115.76 N.