At a particular playground there is a merry-go-round that may be thought of as a flat, solid disk

Question

At a particular playground there is a merry-go-round that may be thought of as a flat, solid disk of mass 137 kg and radius 1.46 m. A child whose mass is 26.3 kg is running toward the outer rim of the merry-go-round so that his path intersects the rim perpendicular to the radius. The child's speed is 2.8 m/s.

A. What is the moment of inertia of the merry-go-round before the child jumps onto its rim or outer edge?

I_mgr =   146.0146 kg·m²

B. What will be the moment of inertia of the merry-go-round and boy system after the boy has jumped onto its outer edge?

I_sys =  202.07568 kg·m²

C. As the child is running toward the merry-go-round, that angular momentum does he have relative to the center of the merry-go-round?

Lchild =  387.5424 kg·m2

s

D. What will be the final angular speed of the merry-go-round after the child has jumped on?

𝜔 =  ? rad/s

I was able to find parts a & b. Part c and d are wrong. Not sure why, could someone please explain?

Answer 1

C. The angular momentum of the child could be found, if we use the formula L_chld = m_chld ·v·R.

We know everything in it. So we find

L_chld = 26.8 kg x 2.8 m/s x 1.46 m = 109.6 kgm²/s

D. The final angular speed of the system after the child jumped on it is ω₂. We can find it using the law of conservation of angular momentum.

Before the child jumped, angular speed of the carousel is ω₁.

We can write

I_mgr x ω₁ = I_sys x ω₂

_

It could be seen that without knowing initial angular speed of the merry-go-round, ω_1, we CANNOT find the final answer. So, please provide this piece of information.

My comment:

Please do not write so many significant digits. Usually three is enough. Even if you write one decimal in your answer, it is not very reliable because the precision of the measurement of the mass of the disk is not big - 137 kg (no decimals).