Do springboard divers violate angular momentum conservation?
by Dae-sun Kang
No. However, divers can perform somersaults and twists even though they have zero angular momentum at all times during the stunt. Also, it a diver is somersaulting in space and possessed angular momentum only about his somersaulting axis.
It is quite wrong to suppose that substantially all twist in diving comes "from the board", as there are number of dives which require gyrations other than twist to be completed before the twist begins. Thus a 1.5 somersault with full twist, the somersaults being completed before the twist begins, is quite possible, as any competent diver will demonstrate. Furthermore, consideration of the diver as a gyroscope shows immediately that if twist is taken from the board simultaneously with somersault then precession of the system about the total angular momentum vector leads to a cart--wheeling or "going over sideways" at the end of the dive. The backward dive, piked with half twist is practically identical with the action of the cat.
The mechanism of twist "not from the board" is really quite simple, but it is easy to fall into the trap of referring the motion first to the axis through the trunk and then to the axis through the legs. Description of the mechanism in there terms is cumbersome, unconvincing and mathematically unwieldy. Furthermore, the diver uses the hips rather than the waist, as his spine is not so pliable.
The simplest way of understanding the mechanism is to think of the way in which children hang from a roe or a tree and, by making a forward sideways and round sweep with the legs, twist
themselves to face the other way (See Fig.1)
Swinging the legs forward merely sets the whole body swinging slightly. As the sideways sweep begins, the system as a whole begins to rotate in the opposite direction in order to conserve angular momentum (initially zero). The net result as seen by an observer on the ground is a sequence of positions similar to the sort of thing seen in experiments with falling cats.
Three further brief points might be made. Firstly, the mechanism is quite independent of any alterations in the moments of inertia of different parts of the body, though the rate of twisting produced will be dependent on the relative moments of inertia of the trunk and legs as well as the angle between the legs and the trunk. Secondly, the motion is very easily understood and considered mathematically if referred always to the axis of the trunk. Thirdly, there is a complication in the movement of the legs which I have not been able to discuss here, but which does not give rise to any substantial mechanical effect; the predominant effect arises from the sweeping round of the legs. Fourthly, control of the twist as in diving is by alteration of the angle at the hips and by extending the arms of holding them to the body. Divers apparently find a near-correct angle instinctively, but often have to amend their technique as
described above, to obtain the exact amount of twist required in competition diving.
Reference:
Zero Angular Momentum, American Journal of Physics vol 54, 1989
The falling cat and the twisting diver, New Scientist, 1960
Springboard divers and angular momentum conservation, American Journal of Physics vol 49, 1979
