Max (15 kg) and maya (12 kg) are riding on a merry-go-round that rotates at a constant speed. max is sitting on the edge of the merry-go-round, 2.4 m from the center, and maya is sitting somewhere between the edge and the center. the merry-go-round is a solid disk with a radius of 2.4 m, a mass of 230 kg, and is rotating at a constant rate of 0.75 rev/s. the system, which includes max, maya, and the merry-go-round, has 8700 j of rotational kinetic energy. how far away is maya from the center of the merry-go-round?

Refer to the diagram shown below.

M = 230 kg, the mass of the wheel

m₁ = 15 kg, Max's mass

m₂ = 12 kg, Maya's mass

r = 2.4 m, the radius of the wheel

Max is located at 2.4 m from the center of the weel.

Let x = the distance of Maya from the center of the wheel.

The polar moment of inertias of the system is

J = (1/2) Mr² (for the wheel)

+ m₁r² (for Max)

+ m₂x² (for Maya)

That is,

J = 0.5 * (230) * (2.4) ² + (15) * (2.4) ² + (12) x² kg-m²

= 748.8 + 12x² kg-m²

The angular velocity is

ω = 0.75 rev/s = (0.75*2π) rad/s = 4.7124 rad/s

By definition, the rotational KE is

KE = (1/2) * J*ω²

Because the rotational KE is 8700 J, therefore

(1/2) * (748.8 + 12x²) * (4.7124) ² = 8700

11.1034 (748.8 + 12x²) = 8700

748.8 + 12x² = 783.547

12x² = 34.747

x = 1.702 m

Answer: 1.7 m (nearest tenth)