In
order to create angular momentum for rotation, an impulse
must be exerted on your body. This is achieved by pulling
down on the bar before you leave, and kicking your legs.
This impulse gives you angular momentum, so once you leave
the bar, you start to twist.
The relative angular velocities of the
layout and the front somersault demonstrate the principal
applied to the ice skater above. The layout is performed
with a straight body, so I about the axis (through the hips)
is very large. Angular momentum is constant throughout,
so a relatively slow angular velocity is achieved. This
slow rate of rotation is very visible to spectators. In
comparison, the front somersault is performed in a tucked
position. I is therefore much less (body is more compact),
and since the starting angular velocity is approximately
the same as in the layout, the angular velocity is much
higher. The faster rate of spin allows double or even triple
somersaults before a catch.
More Advanced Tricks
More advanced tricks on the trapeze involve
a very complicated series of somersaults and twists before
the catch. Although it is possible to twist before a catch,
the movement before you leave the bar is different to that
preceding a somersault, making it very difficult to combine
the two. What the performer needs to do is start to somersault,
and twist while he is in the air.
This may appear to be a violation of the
conservation of angular momentum rule, since the man starts
with no angular momentum about his twisting axis, and during
the flight, he seems to create some. This is not the case.
In order to understand how this is achieved,
we must appreciate that a person is not a rigid object,
and therefore there is only a certain distance that we can
go, using a person modelled as a rod.
Let us assume that the performer leaves
the bar with a large, non-zero angular momentum, this is
a vector parallel to the axis of rotation through his hips,
so he starts to somersault (no twist to start with). Since
this angular momentum is conserved, the vector it corresponds
to remains in the same direction, regardless of how much
the flyer wiggles or squirms. However, the axis about which
the man rotates can change (the axis of rotation is always
in the same direction as the angular velocity vector). In
order to initiate twisting, the flyer 'throws' his arms
round. This causes his axis of rotation to wander off the
direction of the angular momentum vector. This then represents
a threat to the conservation of angular momentum principal,
since the magnitude of angular momentum in any given direction
has changed. This initiates a twist, creating exactly enough
angular momentum so that the vector sum of the two separate
angular momentums is still the same as the original value.
Angular momentum has been conserved, and the flyer has initiated
a twist in mid-air.
It is interesting to note that this is
only possible if the flyer starts with angular momentum.
Some figures can help to demonstrate the relationship between
the angle between the axis of rotation and the angular momentum
vector and the rate of twisting. In a layout (back somersault
with body straight), throwing his arms to create an angle
of just 11o, causes his body to twist at a rate of 3 twists
per somersault.
In a front somersault, when
the flyer's body if tucked or piked, throwing the arms will
create an angle larger than 11o (since I is smaller). For
an angle of 20o, the body will twist at a rate of five and
a half twists per somersault.
In
order to create angular momentum for rotation, an impulse
must be exerted on your body. This is achieved by pulling
down on the bar before you leave, and kicking your legs.
This impulse gives you angular momentum, so once you leave
the bar, you start to twist.
