Show your work and include units with your answers for full credit. A merry-go-r

Question

Show your work and include units with your answers for full credit.

A merry-go-round is essentially a solid disk with a mass of 120 kg and a radius of 1.6 m. A 30-kg child sits on the outside edge of the merry-go-round. The merry-go-round is rotating at 4.8 rad/s.

(a) What is the rotational kinetic energy of the merry-go-round and child together? (Hint: make sure you find the total rotational inertia first)

(b) The child wants to stop the merry-go-round, so he drags his foot along the ground. This applies a tangential force of 29 N to the edge of the merry-go-round. How many complete rotations does the merry-go-round make before it comes to rest? (Hint: what torque does the child supply? How much work does he do? Also, check the units of your answer.)

Explanation / Answer

(a)
Moment of Inertia of Solid disk, Id = 1/2* Mr^2
Moment of Inertia of Child, Ic = m*r^2
I = Id + Ic
I = 1/2*M*r^2 + m*r^2
I = r^2 * (1/2*M+m)

Rotational Kinetic Energy = 1/2*I*w^2
Rotational Kinetic Energy = 1/2 *  r^2 * (1/2*M+m)*w^2
Substituting Values,
Rotational Kinetic Energy = 1/2*1.6^2 * (1/2*120 + 30) * 4.8^2 J
Rotational Kinetic Energy = 2654.2 J

(b)
Torque = F*r
t = 29*1.6 Nm
t = 46.4 Nm

Woek done = Change in K.E = 2654.2 J
W = t*
2654.2 = 46.4 *
= 57.2 rad

1 complete rotation = 2* rad
No of rotations, = 57.2/(2*) = 9.10
Complete rotations does the merry-go-round make before it comes to rest, = 9

Now of rotation's =

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