To answer the question ‘When
performing a round-off back somersault why is it easier when we include a run
up phase?’ the skill needs to be looked at with the run and then without it.
Acceleration, speed and velocity
Gymnasts need to reach a high speed in their run up phase
before the round-off in order to get enough momentum to complete the
tumble. The tumble line is approximately
20 meters. The gymnast would run about 15 m before completing the tumble.
If it took a gymnast 3 seconds to run 15 meters, they would
be running at 5 m∙s⁻¹.
Velocity can be measured as;
V (Velocity) = Δ (change in) S
(speed)/ Δ (change in) t (time)
So the velocity is 5 m∙s⁻¹
The acceleration is found using this equation;
a (acceleration) = Δ(change in) v(velocity)/ Δ(change in) t
(time)
We cannot work out the acceleration because we don’t have
the distance of the runner at each point in time, however to produce a quicker
acceleration the athlete must have a higher change in velocity over the 3
seconds. The gymnast needs to move as quickly as they can so they build up
enough speed and momentum to perform the tumbles.
If we wanted to work out the angular velocity of the back
somersault we would know the angular displacement is 360˚ because the body
rotates a full 360˚ and it would take 0.5 seconds to perform the spin.
So;
Angular velocity (ω) = 360˚/0.5s
Angular velocity (ω) =730˚∙s⁻¹
So the athlete would spin around
twice in 1 second.
This equation is used considering
there was a run up before hand, however if there was not a run up the gymnast
would not be able to complete the back somersault as quickly, it may take the
gymnast 1 second to complete a back somersault this could result in a fall
halfway through the tumble or injury. We know that speed, velocity and
acceleration are important before the tumble is completed but now we need to
look at how to build up momentum to reach the high speed.
The Impulse – Momentum Relationship
Momentum describes how much
velocity something has and how the velocity can become greater. Something or
someone who has a larger mass will move at a greater velocity therefore having
a greater momentum. Momentum can be measured as;
P (momentum) = m(mass) x v(velocity)
Let’s just say if the athlete is
not moving before the round-off they have;
Velocity = 0
P = m x 0
Just say the person had a mass of
60kg
P = 60 x 0
P = 0 kg* m∙s⁻¹ therefore there is
no momentum
However if the person includes a
run up before the round off they have;
Let’s say the average velocity is
5 m∙s⁻¹
P = 60 x 5
P = 300 kg* m∙s⁻¹
To make momentum larger more force
has to be applied to the object. Force and time together is impulse (j). The
equation for this is;
Δ(change in) f(force) X t (time) =
Δ(change in) P (momentum)
This is the impulse-momentum
relationship. Applying this to the round-off back somersault is done in the run
up phase. During the run up the athlete needs to get as much momentum as
possible to gain enough power to perform the round-off back somersault (in
gymnastics height is important when performing tumbles), more momentum will
produce more height. Without the run up phase there is no momentum for the
athlete to gain enough height to do the back somersault. This brings us onto
Newton’s Laws.
Newton’s laws
Newton’s first law does not apply in this context as the
gymnast is already moving. The second law is ‘the acceleration of an object is
proportional to the net force acting on it and inversely proportional to the
mass of the object: F (force) = m (mass) x a (acceleration).’ This was briefly
discussed in the impulse-momentum relationship stating that more force will
result in more momentum. Newton’s third law ‘for every action there is an equal
and opposite reaction’ when feet and hands hit the ground during the round off,
the ground exerts an equal and opposite reaction force, this is called the
ground reaction force (GRF) which will stop the feet and hands from sinking
into the earth. During a round off the hands will hit the ground first, when
the hands push against the ground, the ground will push back against the hands
springing the person up and around to complete the round off. Newton’s third
law is used again when the legs snap together and the feet hit the ground, the
GRF then pushes the feet off the ground resulting in a jump which will then
lead into the back somersault. In order to jump higher we need to exert more
force on the ground so the ground pushes us back up into the air with the same
amount of force.
Kinetic energy
The kinetic energy is associated with motion. It can either
be a linear or angular motion. A gymnast would use both during the round-off
back somersault. The gymnast needs a greater velocity rather than a greater
mass to produce a larger kinetic energy. Gymnasts need to incorporate a run up
in this skill to get a lot of power, therefore a greater velocity and greater
kinetic energy. The kinetic energy is used when the gymnast does the round off
and then goes straight into the back somersault. The faster the gymnast moves
the more energy they will possess. During a floor routine gymnasts will repeat
this move up to 4 times and incorporate other tumbles and acrobatic moves.
Using this kinetic energy information we could find ways for gymnasts to
complete these skills while expending less energy so they don’t get tired after
their first tumbling line.
The equation for kinetic energy is;
KE (kinetic energy) = ½ mv²
