A merry-go-round has I = 319 kg•m? on its own, and is now spinning at 1.22 rad/s with a 34.7 kg kid standing 1.50 m from the axis. The kid then walks inward until he reaches 0.250 m from the axis.

Question

A merry-go-round has I = 319 kg•m? on its own, and is now spinning at 1.22 rad/s with a 34.7 kg kid standing 1.50 m from the axis. The kid then walks inward until he reaches 0.250 m from the axis What is the new angular velocity of the system?

Answer 1

Use conservation of angular momentum I₁ ϖ₁ = I₂ ω₂ where I₁ = 319 kg m² + 34.7(1.5)² = 319 + 78.075 kg m²

I₂ = 319 kg m² + 34.7(.25)² so I₂ =319 + 2.16875 kg m². So I₁ = 397.075 and I₂ =321.16875. Using ω₁= 1.22 rad/s and going back to the equation ω₂ = (397.075 •1.22)/ 321.16875 gives ω₂ 1.512 rad/s for the new angular velocity.