Biomechanics

Law of Conservation of Linear Momentum

Principle states the total momentum of two objects before and after impact are equal.

This occurs in perfectly elastic collisions where no energy is lost through sound or heat.

Momentum - definition

• A measure of the amount of motion possessed by a moving body.

• The greater an object’s momentum, the more force needed to stop or slow the object.

momentum formula

M = mass x velocity

Impulse-Momentum Relationship

The application of force over a period of time to change the momentum of an object.

Impulse = force x time

The longer a force is applied, and the greater the force that is applied, the greater the objects impulse or change in momentum.

Impulse - Increasing Momentum

To maximise the momentum of an object, an individual can increase both the force and time component.

Force: increased through effective summation of force amd improved strength - increased contraction of muscle and more motor unit recruited.

Time: increased through technique and equipment modifications.

Impulse - Decreasing Momentum

To decrease the momentum of an object an individual will look to increase the time component, as the total change in momentum remains constant.

By increasing the time component, the peak force will be decreased, reducing the risk of injury and pain.

Coefficient of Resitution

• Measures the elasticity of the collision between an object and a given surface.

• A measure of how much momentum is conserved pre to post impact between 2 colliding bodies.

• Measured on a scale of 0→1

• The greater the COR, the most elastic the collision is, and therefore less energy is lost during the collision.

Factors Affecting COR - Equipment and Surfaces

• Condition of the balls - new tennis balls have a higher COR compared to an old tennis ball.

• Equipment material - aluminium bats have a higher COR compared to a wooden bat

• Type and condition of playing surface - Clay court has a high COR compared to a grass court

Factors Affecting COR - Temp of balls

An increase in the temperature of the balls results in an increase in the COR.

the particles inside the ball gain more kinetic energy and therefore move faster. This allows the ball to return to its original shape faster, increasing elasticity.

Factors Affecting COR - velocity of the collision

Velocity of the colliding objects can influence the COR.

Increasing velocity increases the energy lost through the collision due to the greater compression of the ball.

Angular Momentum Definition and Formula

Refers to the quantity of angular motion possessed by a rotating body.

AM = Moment of Inertia x Angular Velocity

Moment of Inertia Definition

Refers to the resistance of a rotating object to a change in its state of motion.

Moment of Inertia Formula

MOI = mass of the object x radius of main mass distribution to the axis

Radius of rotation = how the object’s mass is distributed about the axis of rotation

Moving the object’s mass further from the axis you are increasing the radius of rotation and therefore MOI.

Angular Velocity Definition

The rate of change in angular position of a body.

Conservation of Angular Momentum

Indicates a rotating body will continue to rotate indefinitely unless an external force acts on it.

Angular momentum remains constant therefore a high moment of inertia results in a low velocity and visa versa.

Parts of a Lever

Resistance (Output force) = force exerted by the lever

Axis/Fulcrum = the pivot point at which the lever rotates around

Effort (Input force) = the force exerted on the lever

Effort Arm = the distance between the axis and the point at which force is applied

Resistance arm = the distance between the axis and the centre of the resistance

Third Class Lever

The axis is located at one end, with the application of force in the middle, and the resistance applied on the opposite end.

The most common type of lever in the human body:

-muscle attachment = application of force

-joint = axis

-the weight = the resistance

Third Class Levers - Speed Multiplyer

By increasing the length of the lever, it is possible to generate greater velocity/angular momentum of the bat or club resulting in a greater momentum being transferred to the ball.

This is because, in a longer resistance arm, the end of a lever will have a greater displacement over the same time period, therefore increasing velocity.

HOWEVER, increasing the length may increase the weight of the bat/club, which could make the equipment harder to control or generate angular velocity (especially younger children).

Lift Definition

Refers to the component of force that acts perpendicular to the direction of flow.

will act at a right angle to the direction of motion - meaning it can act in an upward and downward motion.

Bernoulli’s Principle

States that as the speed of a fluid increases, the pressure will decrease.

INVERSELY proportional

Magnus Effect and Eccentric force

The term used to describe the effect of rotation on an object’s path as it moves through a fluid. applies Bernoulli’s Principle.

When a ball is struck with an eccentric force linear and angular rotation occurs. The resultant movement (curve) is referred to as the Magnus effect.

Eccentric force = any force that is off center that is applied on an object.

Boundary Layer

A thin layer of air/fluid that is surrounding or ‘attached’ to the ball.