Question

We can model a small merry-go-round as a uniform circular disk with mass 88 kg and diameter 1.8 m. How many 22 kg children need to ride the merry-go-round, standing right at the outer edge, to double the moment of inertia of the system?

Answer 1

Answer:

n = 2 children

Explanation:

Given

M = 88 Kg

D = 1.8 m ⇒  R = D/2 = 1.8 m/2 = 0.9 m

m = 22 Kg

n = ?

We apply the formula

Icm = M*R²/2

⇒ Icm = (88 Kg)*(0.9 m)²/2 = 35.64 Kg*m²

If

I = 2*Icm = 2*35.64 Kg*m² = 71.28 Kg*m²

we apply Steiner's Theorem as follows

I = Icm + n*m*R²

⇒  n = (I - Icm) / (m*R²)

⇒  n = (71.28 Kg*m² - 35.64 Kg*m²) / (22 Kg*(0.9 m)²)

⇒  n = 2 children