The rotating diver

Problem

The rotating diver. A diver jumps off the springboard and performs a somersault in mid-air. During the flight they move their arms and legs. (a) Does their centre of mass follow a trajectory different from the parabola of a point body? (b) Can the sum of their internal angular momenta change while they are in the air? (c) How do they actually use their arms to speed up or slow down the rotation? Argue without calculations.

Solution

(a) No. While the diver is in flight, only weight (an external force) acts on them: the centre of mass follows a perfect parabola, like a point particle. Moving the arms and legs are internal forces that do not shift the CM.

(b) No. In the air there are no significant external torques (weight, applied at the CM, has zero torque about the CM). Hence the internal angular momentum $\vec{L}_\text{int}$ is conserved: its sum cannot change.

(c) By varying the moment of inertia. Since $L_\text{int} = I_\text{CM}\,\omega$ is constant, reducing $I$ increases $\omega$ and vice versa. Tucking in (arms and legs close to the axis) decreases $I$ and the rotation becomes faster; opening out increases $I$ and the rotation slows down. This is how the diver controls the number of rotations and “brakes” before entering the water.

Links

Topics: Centre of mass Concepts: Angular momentum · Conservation of angular momentum · Moment of inertia