If you intend to master biomechanics, then you must have a clear understanding of mechanics. In this page, I will be breaking down concepts of mechanics that pertain to sports medicine such as work and energy, kinematics, torque, and momentum.
What is Mechanics?: Mechanics is a branch of physics concerned with motion and forces producing motion. Forces are fundamental to understand biomechanics as they play a role in how muscles move, why certain stances are appropriate for certain situations, and how to optimally train for specific scenarios to prevent injury.
The Basics: Before going into any topics involving mechanics, it is important that you understand what a vector is. A vector is a quantity that has both magnitude and direction. This is typically represented by an arrow that is both pointing in the angle of the direction and has a length proportional to its magnitude.
Kinematics and Forces
Kinematics: Kinematics essentially aims to describe how an object moves through space and time. Translation kinematics is essentially the motion of any given object without rotation. This would include dropping a ball from the table or throwing a baseball to play catch. The main catch is that the velocity equation is the derivative of the position equation and the acceleration equation is the derivative of the velocity equation (this mean acceleration is the 2nd derivative of the position equation). This is because in Calculus the derivative of any given function is the instantaneous rate of change of a function with respect to a variable (for acceleration, velocity, and position, this variable will be time). Taking this into account, velocity is defined as the change in position over a period of time and acceleration is defined as a change in velocity over a period of time. Rotational kinematics involves the movement of an object when rotation is involved (ie turning the car left or a tetherball rotating around the pole).
Dynamics: Dynamics, on the other hand, aims to explain why things move the way they do and plays a key role in biomechanics. To start, we will look at Newton’s Three Laws:
- An object in motion stays in motion unless an outside force acts upon it.
- F = ma
- Every interaction has an equal and opposite reaction.
Keep in mind that force doesn’t tell us much about the actual motion but changes in motion.
Normal Force: Gravitational force is the force gravity exerts on an object while the normal force is the component of contact force that is perpendicular to the surface of contact. Thus, normal force is a response fore. Essentially, if we apply Newton’s Third Law, this means that normal force is the equal and opposite reaction that occurs when you have a contact force (ie if when a runner strikes the ground, there is a force exerted into the ground by the foot AND a force exerted up the leg by the ground in response. The response force up the leg is normal force). Normal force is crucial in biomechanics and plays a role in many lifts, motions, and in some cases injuries. For starters, we need normal force simply to move. During activities like running or walking, the normal force from the ground onto the feet essentially propels us forward. Without the upward push, movement would be impossible. In addition, normal force plays a role in injuries and joint decay. For example, when running, the normal force exerted into the body is often several times the runner’s bodyweight due to the acceleration involved in the running gait. Thus, knowledge of these normal forces and how they are distributed is crucial for two reasons. First, companies and researchers can make technology like running shoes that can either better redistribute the force over a larger area, or dissipate some of the energy before it enters the feet if they understand these forces. Second, researchers, doctors, and athletes can identify specific movement patterns that either A) engage different muscles or B) increase injury based on the distribution of forces. Thus, athletes, doctors, and researches can adjust their own or other’s movement patterns to either optimize their movement patterns.
Apparent Weight and Normal Force: Generally speaking, normal force is equal to the force exerted on an object by gravity if the object is on a horizontal surface and at rest. If the object is on an inclined surface, then the normal force becomes the gravitational force * cos(theta) if theta is the incline angle. This is because gravity is broken up into two components: one perpendicular to the surface (the normal force) and one parallel to the surface (this may cause the object to slide depending on the other forces present). In these situations, normal force does not have too much of an affect on the object other than balancing out the portion of gravity that is perpendicular to the surface of contact. However, normal force begins to play a different role if the object is moving. Imagine you are standing in an elevator on your way to a work meeting. When the elevator goes up, you may feel like your organs are compressing. When the elevator goes down, you will feel like your organs are stretching out. This is because your apparent weight is changing when the elevator moves. When you step on a scale, the scale measure the normal force being exerted upon you by the ground. If you were to put the scale in the elevator and measure your weight while you were going up, the scale would read higher than if you were in your bathroom. This is because the elevator accelerates upwards towards whatever floor you are trying to reach. Hence, there is a net upward force being exerted upon you, so the normal force equation changes to Gravitational Force + (Your Mass * The Acceleration of the elevator). This same equation can also be used when the elevator is going down because acceleration will be negative.
I’ve drawn a free body diagram on the right to better illustrate this concept.
Torque: If force is what causes linear acceleration, then torque is what causes angular acceleration. Essentially, torque causes something to rotate about an axis. Imagine twisting a doorknob to open a door. When you apply force to the doorknob to open it, you are actually applying torque. Torque is modeled by the equation r*F*sin(theta). Essentially, the two main components of torque is the force applied (F) and the distance from the center of the axis you apply it (r). For example, as far as translational motion goes, the fastest recorded speed sits around 27 mph; however, the average male golfer reaches a club head speed on 93 mph. This is because golfers increase their lever arm by using a golf club, this allowing them to apply more torque onto the ball. Torque is key in many sports, especially in the context of muscles interactions as well as sport motions. For starters, when you simply bend your arms, the biceps apply an upward force some distance away from the elbow joint which creates a torque that bends the arm upward. The amount of torque a muscle can produce is often influenced by its size, angle at which force is applied to the bone, and the length of the lever arm (distance from the joint axis to where the force is applied). This becomes especially important when looking at joints as joints are the pivot points in the body where bones meet. During dynamic physical activity, torque applied to the joints increases due to muscle interactions as well as external forces like normal force or centripetal force (This is the force that keeps an object moving in a circular path). Excessive or improper distribution of torque on muscle can lead to injury. For example, a sudden, quick twist of the knee joint with the foot planted can put excessive stress on the knee joint and even lead to ACL injury.
Momentum and Energy
Momentum: Momentum is the quantity of motion of a moving object. This is calculated by mass * velocity. To break this down, something has momentum when it tends to do something and continues doing it. For example, if you are driving your car on a highway, you have momentum; however, the moment you stop for gas, you lose all momentum. With momentum there are elastic collision and inelastic collisions. Elastic collisions occur when two objects collide and bounce off each other while inelastic collisions occur when the two objects stick together. According to the laws of conservation of momentum, the momentum before the collision must be equal to the momentum after the collision. Impulse is essentially the change in momentum. This can be modeled by Force * Change In Time which equals the change in momentum. I’ve included a derivation of this equation below (Remember that Change in Momentum is equal to Change in Time * Force). Several contact sports and recreation game require the concept of momentum, particularly collisions, to score or gain an advantage against the opponent. For example, in gridiron football, a running back must be both bulky and able to generate significant speed in order to blow through the countless defenders trying to tackle them. Because a tackle is an inelastic collision, the momentum of the running back will decrease with each hit of a defender. Momentum and impulse also play a role in injury science. For example, helmets and padding have shock absorbing qualities that are meant to increase the amount of time over which the force is applied. Because momentum has to stay constant, the force that is actually applied to the body will decrease if the time it’s applied over increases.
Work: Work occurs when an object is displaced by an application of force and is formally defined by the product of the distance over which the force is applied and the actual force that is applied. This is modeled by Force * Displacement * cos(theta) where theta is the angle between the applied force and direction of displacement. Work is the fundamental physics concept behind lifting as it provides a framework into understanding energy expenditure in lifting. For example, for moves that go straight like overhead barbell press, work is being done against gravity and the height of the lift is the displacement. Because the direction of the displacement (upwards) and force (also upwards) are the same, then theta takes a value of 0. This simplifies the work equation to Force * Displacement.
Energy: There are two types of energy: potential and kinetic. Potential energy is the capacity of an object to perform work because of its position. Essentially, an object that is on the ground will have less potential energy than an object that is above the ground because the object above the ground has the potential to fall and accumulate momentum (This illustrates gravitational potential energy which is potential energy an object has because of its position relative to a surface). GPE is modeled by Mass * Gravitational Acceleration * Height of the Object. Kinetic energy is energy associated with motion which is modeled by the equation 0.5 * Mass * (Velocity)^2. Given these equations, it can be said that the change is work is equal to the change in potential or kinetic energy. I had mathematically displayed this below (For the kinetic energy equation, the cos(theta) is not important because we assume that the force and displacement vectors are pointed in the same direction).
Similar to work, energy plays a role in sports and lifting because it contributes to the overall framework of energy expenditure.