Question

A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg·m2. When one person is standing on the carousel at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.600 rad/s. However, as this person moves inward to a point located 0.905 m from the center, the angular velocity increases to 0.800 rad/s. What is the person’s mass?

Answer 1

m = 35.98 Kg ≈ 36 Kg

Step-by-step explanation:

I₀ = 125 kg·m²

R₁ = 1.50 m

ωi = 0.600 rad/s

R₂ = 0.905 m

ωf = 0.800 rad/s

m = ?

We can apply The law of conservation of angular momentum as follows:

Linitial = Lfinal

⇒ Ii*ωi = If*ωf (I)

where

Ii = I₀ + m*R₁² = 125 + m*(1.50)² = 125 + 2.25*m

If = I₀ + m*R₂² = 125 + m*(0.905)² = 125 + 0.819025*m

Now, we using the equation (I) we have

(125 + 2.25*m)*0.600 = (125 + 0.819025*m)*0.800

⇒ m = 35.98 Kg ≈ 36 Kg