# Physics for Sport Performance

Basic principles of physics form the foundation for our everyday lives and activities. Training is no different. To be good in training, you have to be good in elementary physics. Newton’s laws rule the show.

## Newton’s 1st Law – The Law of Inertia #

An object at rest stays at rest or an object in motion will stay in motion at a constant velocity unless acted upon by an external force.

The tendency for an object to remain stationary or in motion at a constant velocity is called inertia. Everything with a mass has an inertia. The heavier the object, the larger its inertia, and the more force is needed to change its velocity. This outlines the importance of force in all movements. In sports, starting, stopping, changes of direction all require us to overcome the inertia of ourselves to complete the movement. Athletes have to produce force in various ways to achieve that. To stop, you have to produce forces to oppose your movement. To speed up, you have to produce force to add to your movement.

## Newton’s 2nd Law – The Law of Acceleration #

Force is the product of mass and acceleration (F=ma).

Acceleration is the change in velocity over change in time (a=∆v/∆t). Velocity is the change in distance over change in time (v= ∆d/∆t). In other words, velocity is simply the displacement of an object in relation to time.

The acceleration of an object is directly dependent on the mass of the object and the amount of force applied to accelerate the object. Change in acceleration will result in the change of velocity of the object. This law forms the basis for training. The heavier the load is, the slower it will move. The more force we can apply to the same load, the faster the load will accelerate, thus the bigger the increase in its velocity. Based on the force formula, we can start to establish optimal loading parameters. If the load is too high, the acceleration will fall off to the extent at which the mass cannot offset the drop in acceleration, thus resulting in a decline in force production. Force production will also decline if the load is too low, as the acceleration will not be able to make up for the decrease in load.

In a sport performance setting, we also need to consider the time-constrained nature of competition. As we have limited time to produce force, the rate of force development becomes crucial. We have to maximize our ability to create the most amount of force in the least amount of time.

This leads us to the impulse-momentum relationship which is Newton’s 2nd law considered in relation to time. Impulse is the amount of force applied over time (J= F∗∆t) and momentum is simply mass ∗ velocity. Impulse equals the change in momentum. As mass is often constant in sport, impulse really dictates the change in velocity of an object (F∗∆t=m∗∆v). The momentum a person can generate or dissipate is dependent on how much force can be applied and how long that force can be applied for. The relevance of this can clearly be seen in most field and court sports. If an athlete goes into a change of direction movement, they go into it with a certain amount of momentum. It takes force to slow and stop that momentum, to then be able to turn it into a new direction. It takes time to complete that movement. If the athlete has the ability to apply greater force quickly, they will complete the change of direction movement faster. If the athlete lacks the ability to produce high force quickly, the movement will require more time as only low amounts of force can be applied.

## Newton’s 3rd Law – The Law of Reaction #

For every action, there is an equal and opposite reaction.

If an athlete performs a jump, force will be applied into the ground. The same amount of force will act back on us in the opposite direction. These forces are called ground reaction forces. These are what make us move. In sprinting, our feet apply force during ground contact. The resulting force in the opposite direction determines our acceleration. The same applies to jumping. If I push into the ground with a certain amount of force, the reaction force will act on my body to make it move upwards off the ground.

Why does all of this matter? As stated, the 2nd law really forms the basis here. The impulse-momentum relationship is an essential consideration in sports. Changes of velocity are inherent in most sports. The successful athlete will be able to effectively control the application of impulse, and thus also changes in velocities required for success.

Athletes have to focus on developing the ability to produce large forces in short amounts of time.

What is important to consider is that force is contextual. Production of force is specific to the manner in which it has been previously trained. As such, force production is also specific to the velocity at which it is produced. If you take an athlete and train them to produce more force (to accelerate faster if the mass is unchanged), they would develop to complete the trained movement at a higher velocity. Being able to complete the movement at a higher velocity puts the athlete in a situation to once again learn to produce force at that higher velocity of movement to get even faster. The climb would continue.

The training process has to continuously progress to allow the athlete to consistently be able to produce higher levels of force at higher movement velocities. For simplicity, we can split this into 3: force production at low, moderate, and high velocity.

## Force production at low velocity #

Low velocity force production, also referred to as maximal strength, is the initial stage of athlete development. At this point in time, all they need is to improve their overall force production capabilities.

Force production at low velocity is the fundamental aspect of all movements.

Referring back to Newton’s 1st law, a stationary object will tend to remain stationary unless acted upon by an external force. The athlete has to be able to develop force from zero velocity (stationary) to make the object (their own body or a specific sport’s instrument) move in the first place. In other words, the athlete must possess adequate maximal strength capacity for their specific sport.

If the athlete is weak and doesn’t have the ability to produce force at zero and low velocity, speed training will just make them produce this weakness faster.

This is the stage in which heavy lifts, often relatively unspecific to the sport to allow for high force production, would be implemented into the athlete’s training plan. Anything in the intensity range of 80-100% 1RM (one-repetition-maximum) lives here.

That could include isometric training. Isometric training refers to static resistance training where no change in the length of the muscle takes place during a muscular action. An example could be a maximal voluntary muscle action at 100% against an immovable object. More specifically, this could be a barbell back squat performed inside a squat rack with the safety pins set at a specific height to allow for maximally pushing the barbell into the safety pins for a set duration of time. Isometric training would aid in developing force from zero velocity to overcome the inertia of the object to be moved.

## Force production at moderate velocity #

As the athlete develops their maximal strength, their training should progressively advance towards higher velocities and more specific training modes.

Force output will always be higher at low velocity. High force output at low velocity serves as the foundation for all increased speed availability. As velocity increases, the ability to apply force and accelerate an object will decrease.

At moderate velocity, we aim at improving the athlete’s ability to produce high forces at submaximal loads. One way to achieve this goal is to utilize moderate-load exercises in the 60-80% 1RM range. The emphasis would be placed on completing the repetitions with maximal intent. The athlete would be coached to explosively accelerate the weight to achieve high force output. This is where quality of repetitions is paramount and fatigue is our enemy, as it would take away from our ability to maximally accelerate the load. Thus, less repetitions in a set and longer rest periods are essential.

This section could also incorporate weighted jump variations. The ballistic nature of jump exercises allows for acceleration throughout the full range of motion to the point at which you leave the ground.

Alternatively, accommodating resistance methods (using resistance bands or chains to increase the resistance of the load through the range of motion) could be implemented. Using accommodating resistance methods would allow for a longer acceleration phase on non-ballistic conventional exercises that would otherwise not be possible.

It is again worth reminding that if the athlete doesn’t have an adequate strength base at low velocities, they won’t be able to produce enough force to create high velocities.

## Force production at high velocity #

As we progress towards higher velocities of movement at higher sport specificity, we want to arrive at the ability to produce high amounts of force with minimal time requirements as determined by the specific sport’s needs.

In relative terms, this force output will be lower than for the two previous stages, simply because there is not enough time to produce that high force. Regardless, this is exactly the environment most sports require.

A successful athlete will be able to quickly accelerate an object (their own body or a specific sport’s instrument) to produce high velocity with a minimal time requirement.

At this stage, they should possess an adequate foundation in force production capabilities. Now they have to learn to apply extreme levels of acceleration in the shortest time frames. The training in this stage would target high movement velocity. This could include lifting light weights explosively, low load ballistic exercises, different jump variations and plyometrics, and sprint and agility training.

There are a few ways to fit all of this into an athlete’s season plan and for that, the specific context along with the competitive schedule needs to be considered. In general terms, more sport specific work would be emphasized closer to the competition (that is often the high velocity work), whereas maximal strength would be focused on further away from competitive scenarios and trained enough to maintain it during the competitive season. Long competitive seasons can call for a concurrent approach to training, where several qualities need to be developed all at once.

It’s important to notice that I’ve explained the concepts from a “single-effort” point of view. What needs to be emphasized is that sport movements are often cyclical. What that means is that this acceleration cycle from low to high velocity occurs many times over the athlete’s competitive effort as they transition through a variety of movements and continuously change directions. As such, conditioning is important to be able to repeat those specific strength qualities in the context of the given sport. Whereas this goes beyond the scope of this article, specific energy system development is crucial for performance.

## Power #

A popular concept to consider in relation to force production at various velocities is power (force ∗ velocity). Some people in the field don’t shut up about it. It is the amount of force one can express at a given velocity.

Each of the 3 broadly defined velocity categories above could produce a range of power outputs depending on the specific forces and velocities produced. As you move up on the velocity sliding-scale, velocity contribution towards power output increases, while force contribution lessens.

While undoubtedly important for sport performance, power as a concept has to be considered in relation to all the physics we have discussed above. Unfortunately, too often it is taken out of context and misinterpreted by people who failed 7th grade physics. That is exactly the reason why I have taken the time to go over the basics first before even mentioning power. It’s a common misconception that power training (by the most simplified definition - training explosively at submaximal loads, often via the use of ballistic exercises) rules all, and maximal strength training is useless for athletes that need to move fast as it will make them slower. That's just wrong.

Power is merely the product of force and velocity. Referring back to the impulse-momentum relationship, you can’t have a velocity without some force preceding it that has acted upon a mass to produce that change in velocity in the first place. Velocity isn’t an independent phenomenon. It’s the maximal force production ability at low velocities that makes high power outputs possible.

Force precedes velocity. Without force, there is no velocity. Without velocity, there is no power.

It might take you a few reads to digest all of the information presented here. And that’s fine. It’s not supposed to be easy. In reality, this article is in many ways already an oversimplification of what’s really going on. It completely overlooks the importance of motor patterns, joint kinematics, and force absorption capabilities. It’s too much to throw into a single article. Regardless, it should still give you an overview of some of the physics and training implications that go along with it.

Hopefully you got some value out of this.

As always, feel free to hit me up with criticism. That's the way to improve.