Simulation · Physics · Class 11

Spin chair: pull in, spin up

From the lesson Angular momentum and its conservation in System of Particles and Rotational Motion. Change the values and watch what happens.

The idea behind it

NCERT §6.12, §6.12.1

Take one particle at distance r⊥ from the fixed axis: the part of its angular momentum along the axis is mr⊥²ω. Adding over the body gives L_z = Iω.
For a particle, l need not be along the axis: l and ω are not necessarily parallel, unlike p and v, which always are.
If the axis is a symmetry axis of the body, the perpendicular parts of the particles' angular momenta cancel in pairs, and L = Iω exactly along the axis.
For a fixed axis, dL_z/dt = τ along the axis, while the component of L perpendicular to the axis stays constant. With I constant this gives τ = Iα again.
Conservation: if the external torque about the axis is zero, Iω = constant. If I decreases, ω increases in the same ratio, and the other way round.
A person on a frictionless swivel chair spinning with arms folded slows down on stretching the arms out (I increases) and speeds up again on pulling them in.
Acrobats, divers, skaters and dancers doing a pirouette on the toes of one foot use this: pulling the arms and legs in reduces I and raises the spin rate.
Kinetic energy ½Iω² = L²/2I is not conserved when I changes: pulling the arms in raises it, and the extra energy comes from the work done by the person's muscles.

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