Rotational momentum and energy

Question

A father gently places his son on a rotating merry-go-round. The merry-go-round is essentially a disk with a mass of 250 kg and a radius of 2.5 m initially rotating at one revolution every 5.00 seconds. Assume the boy has a mass of 12.0 kg and is placed (without slipping) near the edge of the merry-go-round. Determine the final angular velocity of the merry-go-round/boy system.

Answer 1

I will explain how to solve this, but YOU do the calculations.  Use conservation of angular momentum.

 

R = radius of disk

 

I₀ = moment of inertia of merry-go-round (look up the formula for I of a disk of known mass and radius)

 

m = mass of boy

 

ω₀ = initial angular velocity of the merry-go-round = (2π radians)/(5.00 sec)

 

I = moment of inertia of merry-go-round/boy system

 

I = I₀ + mR²

 

ω = final angular velocity of the merry-go-round/boy system = ?

 

Conservation of angular momentum:

 

I₀ω₀ = Iω ⇒

 

ω = I₀ω₀/I =  I₀ω₀ / (I₀ + mR²)

 

ω = I₀ω₀ / (I₀ + mR²)

 

Plug in the moment of inertia of the disk, and the other given numbers, and get the final answer.