An ice skater has a moment of inertia of 5.0 kg ∙ m² when her arms are outstretched,and at this time she is spinning at 3.0 rev/s.If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m²,how fast will she be spinning? A)2.0 rev/s B)3.3 rev/s C)7.5 rev/s D)10 rev/s

Question

Quizplus · Accepted Answer

The conservation of angular momentum is applicable here, which states that the angular momentum remains constant when no external torque acts on a system. Mathematically, I1ω1 = I2ω2, where I is the moment of inertia and ω is the angular velocity.

When the ice skater pulls in her arms, her moment of inertia decreases while her angular velocity increases to balance angular momentum.

Hence, I1ω1 = I2ω2 can be rewritten as ω2 = I1ω1/I2

Substituting the given values, we get ω2 = (5.0 kg ∙ m² ∙ s⁻¹ × 3.0 rev/s) / (2.0 kg ∙ m² ∙ s⁻¹) = 7.5 rev/s

Therefore, the ice skater will be spinning at 7.5 rev/s when she pulls in her arms. Thus, option C is correct.

An Ice Skater Has a Moment of Inertia of 5