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