A figure skater is spinning with an initial angular speed of 9.4rad/s. He then pulls his arms in, reducing his moment of inertia to 0.30 times its original value.

Question

What is his angular speed after pulling in his arms?

Answer 1

This problem utilizes the principle of conservation of angular momentum. We first take note of the given quantities:

Initial angular velocity ω₁ = 9.4 rad/s

Initial moment of inertia I₁ = I

Final moment of inertia I₂ = 0.3I

We then identify the unknown quantity:

Final angular speed ω₂ = ?

We can use Newton's second law for angular acceleration. Since there are no external torques applied, the angular acceleration is zero:

τ = Iα = 0

Therefore, angular momentum is conserved:

L = Iω = constant

I₁ω₁ = I₂ω₂

We rearrange to isolate and solve for ω₂:

ω₂ = I₁ω₁/I₂ = (9.4 rad/s * I) / (0.3I)

ω₂ = 31.3 rad/s