No External Torque Means Iω Stays Constant: Track What Happens to I

If the Earth lost its atmosphere suddenly its moment of inertia would drop, so ω would rise and the day would become shorter. An ant walking along a diameter of a rotating disc from one edge to the other first reduces I (so ω rises) while approaching the centre, and then raises I again (so ω falls). A person of 50 kg who steps from the centre of a turntable (I = 100 kg m², one turn in 2 s) to 2 m away makes I = 100 + 50 x 4 = 300, so ω falls from π to π/3 rad/s. A sphere whirled on a string, with the string pulled so that the radius halves, has I reduced to a quarter, so ω becomes four times, 3ω going to 12ω.

A sphere whose radius grows freely in space keeps its angular momentum, though ω, I and the rotational energy all change.

A man walking around the edge of a freely turning platform makes the platform turn the opposite way so that the total angular momentum stays zero.

When a non-rotating disc of moment of inertia I2 is placed on a spinning disc of I1, ω' = I1 ω / (I1 + I2). For two discs of equal I spinning at ω1 and ω2 and then joined, ω' = (ω1 + ω2)/2, and the kinetic energy lost to the interaction is (1/4) I (ω1 - ω2)². Angular momentum is conserved in such collisions but kinetic energy is not.