Question

consider a person sitting on an office chair that is free to spin around its center. assume the swiveling mechanism is nearly frictionless. the person is initially spinning with her arms stretched out away from their body. what happens when the person pulls her arms closer to their body as she spin, and why?

Answer 1

When a person in a frictionless spinning chair pulls their arms in, their spin rate increases due to the conservation of angular momentum, with their decreased moment of inertia leading to an increased angular velocity.

Step-by-step explanation:

When a person pulls their arms closer to their body while spinning on a nearly frictionless office chair, the rate of spin increases due to the conservation of angular momentum. Angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω), expressed as L = Iω. When the arms are brought closer, the moment of inertia decreases (I' < I), but because angular momentum must stay constant (L = Iω = I'ω'), the angular velocity (ω') must increase to balance the equation. Additionally, the work done by pulling the arms inward converts into increased rotational kinetic energy, as no energy is lost due to the frictionless environment. If the person extends their arms out again, they will return to their original angular velocity.