Biomechanics and Linear Motion Notes

Biomechanics Introduction

Biomechanics is the science behind technique, helping athletes and coaches refine techniques and correct performance errors.
Top performers use biomechanical analysis to enhance their technique.
High-quality techniques reduce stress on the musculoskeletal system, lowering the risk of injury.
This section covers five chapters on biomechanics, revisiting motion mechanics and detailing the field.
Concepts were introduced in Chapter 2 of OCR AS PE, so reviewing it is recommended.
The final chapter focuses on critically evaluating efficient performance in physical activities.
No advanced math skills are needed, focusing on definitions rather than complex calculations.
The goal is to foster an appreciation for biomechanics and its application to improve performance and exam scores.
Learning objectives include understanding Newton’s laws, force and motion, mass, inertia, momentum, linear motion, distance, displacement, speed, velocity, acceleration, and interpreting motion graphs.

Linear Motion

This chapter explores mechanical concepts related to linear motion, where a body’s center of mass moves in a straight or curved line.
Key concepts include Newton’s laws of motion, mass, inertia, and momentum.
Linear motion is described using measurements like distance, displacement, speed, velocity, and acceleration.
Analyzing linear motion helps when visual observation alone is insufficient, such as in the 100m sprint.
Data is presented in graphical form for interpretation.

Newton’s Laws of Motion

Newton’s laws explain the relationship between motion and force.

Linear Motion

Linear motion occurs when a body moves in a straight or curved line, with all parts moving the same distance, direction, and speed.
Example: A skeleton bobsleigh moving down straight and curved parts of the track.

Force

Force is a push or pull that alters the state of motion of a body.

Inertia

Inertia is the resistance of a body to change its state of rest or motion.

Newton’s First Law of Motion - The Law of Inertia

'A body continues in a state of rest or of uniform velocity unless acted upon by an external force.'
Often referred to as the law of inertia.
Inertia means laziness in Latin.
Everything in the universe is lazy; force is needed to initiate movement, and once in motion, further force is required to change its speed or direction.
Explains that a stationary body remains at rest until an external force is applied. Example: A netball stays in the center's hands until force is applied to pass it.
A moving body continues at constant velocity until an external force changes its speed or direction. Example: A netball continues until caught, and its direction changes when another player applies force.

Newton’s Second Law of Motion - The Law of Acceleration

'When a force acts on an object, the rate of change of momentum experienced by the object is proportional to the size of the force and takes place in the direction in which the force acts.'
Any change in velocity is directly proportional to the force applied and occurs in the direction of the force.
Example: A netball shooter near the goal applies a small force, while one at the edge of the circle applies a larger force.
Force = mass \times acceleration or F = ma

Momentum

The quantity of motion possessed by a moving body.
Momentum = mass \times velocity, measured in kg \cdot m/s

Acceleration

The rate of change of velocity.

Newton’s Third Law of Motion - The Law of Reaction

'For every force that is exerted by one body on another, there is an equal and opposite force exerted by the second body on the first.'
For every action, there is an equal and opposite reaction.
One force is the action force, the other is the reaction force.
Example: A netball player bounce passing exerts a downward action force, and the ball exerts an upward reaction force.
The ball exerts a downward action force on the ground, which exerts an upward reaction force on the ball, causing it to bounce.
Forces do not cancel each other out because of the difference in mass between the two bodies; the larger the mass, the smaller the effect of the force and the less the acceleration.
Example: When a netball bounces, the court’s large mass means the reaction force on the ball is significant, but the action force on the court is negligible.
In most sporting examples, mass remains constant, so a change in momentum is due to a change in velocity.
F = ma is used to calculate the size of a force, measured in Newtons (N).

Action Force

A force exerted by a performer on another body. Example: A sprinter's backward and downward force on the blocks.

Reaction Force

An equal and opposite force to the action force exerted by a second body on the first. Example: The blocks' forward and upward force on the sprinter.
Motion in sport requires an external force; there is no motion without force.
Force without motion occurs when opposite forces are balanced. Example: A gymnast in a handstand exerts a downward action force, and the bar exerts an upward reaction force, resulting in no movement.

Mass, Inertia, and Momentum

Mass

Mass is the amount of substance in a body, measured in kilograms (kg).
A larger body contains more mass.

Inertia

Inertia is the reluctance of a body to change its state of motion.
Bodies want to remain at rest or continue moving at the same velocity.
From Newton’s first law, a force is required to change this state of motion.
Inertia is directly related to mass; the bigger the mass, the larger the inertia, and the greater the required force to change its motion.
Example: Lighter bowling balls are easier to send towards the skittles than heavier ones.
Applying equal force to a javelin and a shot put will result in greater acceleration of the javelin.
Greater energy is needed to start and build velocity than to maintain it.
A body with greater inertia requires a larger force to change direction.
Sports requiring quick changes of direction often involve smaller, lightweight performers.
Weight categories in contact sports account for differences in inertia.

Momentum

Momentum is the quantity of motion possessed by a body and is ‘mass on the move’.
Depends on mass and velocity.
Momentum = mass \times velocity (Mo = mv)
A stationary body has no momentum.
Changes in momentum are due to changes in velocity, as mass remains relatively constant.
A sprinter has greater momentum at 70m than at 10m due to higher velocity.
Momentum is crucial in collisions; greater momentum results in a more pronounced effect on the other body.
In rugby, players with large mass and high velocity generate considerable momentum, making them hard to stop.

Describing Linear Motion

Measurements used to describe linear motion include mass, distance, displacement, speed, velocity, and acceleration.
Each quantity needs a simple definition, a relevant equation, and a unit of measurement.

Distance

The path taken in moving from the first position to the second, measured in meters (m).

Displacement

The shortest straight-line route between two positions in a stated direction, measured in meters (m).

Distance versus Displacement

Distance is the length of the path taken by a body in moving from one position to another.
Displacement is the shortest route from start to finish.

Speed

A body’s movement per unit of time with no reference to direction, measured in meters per second (m/s).

Velocity

The rate of motion in a particular direction; the rate of change of displacement, measured in meters per second (m/s).
Velocity (m/s) = displacement (m) / time taken (s)
Velocity can change when direction changes, even if speed remains constant.

Speed versus Velocity

Speed is the rate of change of distance.
Speed (m/s) = \frac{distance (m)}{time taken (s)}
Velocity is the speed of a body in a given direction and is the rate of change of displacement.
Velocity (m/s) = \frac{displacement (m)}{time taken (s)}

Acceleration

The rate at which a body changes its velocity, measured in meters per second squared (m/s^2 or ms^{-2}).
Acceleration (m/s^2) = \frac{change in velocity (m/s)}{time taken (s)} = \frac{vf – vi}{t}
where:
v_f = \text{final velocity (m/s)}
v_i = \text{initial velocity (m/s)}
t = \text{time taken (s)}

Deceleration

The rate of decrease in velocity, often referred to as negative acceleration, measured in meters per second squared (m/s^2 or ms^{-2}).
Zero acceleration means a body is at rest or moving with constant velocity, with a net force of 0N.

Graphs Of Motion

Graphs help visualize and understand motion, presenting information quickly, like in sprints.
Two main types: distance/time graphs and velocity/time graphs (or speed/time graphs).
Velocity/time and speed/time graphs are treated similarly.
The shape of the curve indicates the pattern of motion at a specific time.

Distance/Time Graphs

Indicate the distance traveled by an object over time.

Gradient of Graph

The slope of a graph at a specific moment.
Gradient = \frac{change \space in \space y \space axis}{change \space in \space x \space axis}
Plot distance on the y-axis and time on the x-axis.
The gradient indicates whether the body is stationary, moving at constant speed, accelerating, or decelerating.
horizontal line = no motion
positive curve = acceleration
regular diagonal line = constant speed
negative curve = deceleration
gradient of curve = distance / time = speed

Velocity/Time Graphs

Indicate the velocity of an object over time.
Plot velocity on the y-axis and time on the x-axis.
The gradient indicates whether the body is moving at constant velocity, accelerating, or decelerating.
horizontal line = constant velocity
positive curve = acceleration
negative curve = deceleration
a curve or line below the x axis = change in direction
gradient of curve = change in velocity / time = acceleration