Question

a person stands, hands at side, on a platform that is rotating at 1.24 rev/second. if the person now raises his arms to a horizontal position, the speed of rotation decreases to 0.86 rev/second. by what factor has the moment of inertia changed?

Answer 1

The moment of inertia of a person standing on a rotating platform increases by a factor of approximately 1.44 when the person raises their arms from their side to a horizontal position.

Step-by-step explanation:

The question asks about how the moment of inertia of a person changes when they move from having their arms at their sides to extending them horizontally while standing on a rotating platform. The speed of rotation decreases from 1.24 rev/second to 0.86 rev/second when the arms are raised.

To find by what factor the moment of inertia changes, we can use the conservation of angular momentum, which states that the initial angular momentum (L₀) is equal to the final angular momentum (L₁) assuming no external torques are acting on the system:

• L₀ = L₁
• I₀ ⋅ ω₀ = I₁ ⋅ ω₁

Where I₀ and I₁ are the moments of inertia before and after the arms are raised, and ω₀ and ω₁ are the respective angular velocities. Solving for the factor change in moment of inertia, we get:

• Factor of change in I = I₁ / I₀ = ω₀ / ω₁
• Factor of change in I = 1.24 / 0.86
• Factor of change in I ≈ 1.44

Thus, the moment of inertia increased by a factor of approximately 1.44 when the person raised their arms.