Notes · Physical EducationUK · A-Levels

Biomechanical Movement

This chapter applies the mechanics of forces to sporting movement. It states Newton's three laws and applies them to sporting actions, defines force and shows how to draw free-body diagrams and interpret ground reaction force and impulse, explains how the centre of mass governs stability, and analyses the three classes of lever and their mechanical advantage - always with the full, recomputed calculations the examination demands.

4 sections~17 min reading time3 competenciesLevel Standard 3 · Advanced 1

T·0555 / 17

Exam profile

AO1 · State Newton's laws, define force and describe the three lever systemsAO2 · Apply the laws, draw free-body diagrams and analyse levers in sporting actionsAO3 · Analyse and evaluate movement, calculating F = ma, moments and mechanical advantage

Operators:stateexplainapplycalculateanalyseevaluate

basic level

AS-Level requires Newton's laws, the definition of force, free-body diagrams and the three classes of lever.

higher level

The full A-Level requires impulse from force-time graphs, the analysis of the centre of mass and stability, and the calculation of mechanical advantage.

Depth

Text

Contents · 4 sections

Biomechanical Movement

Newton's laws of motion in sport#

StandardAQA 7582 3.2.3.1DfE GCE PE - Newton's laws of motion

Ground reaction force in a sprint start

Fig. 1The sprinter pushes down and back on the ground (action); by Newton's third law the ground pushes up and forward on the sprinter (the ground reaction force), whose resultant with weight and air resistance accelerates them up and forward.

Newton's three laws describe how forces change motion, and every one of them can be seen in sport. The first law (inertia) states that a body continues at rest or moving at constant velocity unless acted on by an external resultant force. A football sitting on the penalty spot stays there until the boot applies a force; a curling stone would slide forever at constant velocity were it not for the friction of the ice - the resultant force is what changes the state of motion.

The second law (acceleration) states that the rate of change of momentum of a body is proportional to the resultant force and takes place in the direction of that force; for a constant mass this reduces to the familiar

F = ma

. This is the most quantitative of the laws: the acceleration of a sprinter, a shot or a ball is directly proportional to the resultant force applied and inversely proportional to its mass, which is why a greater force produces a greater acceleration and why lighter implements accelerate more for the same force.

The third law (action-reaction) states that for every action there is an equal and opposite reaction: when a body exerts a force on a second body, the second exerts an equal and opposite force on the first. A sprinter drives their foot down and back into the blocks (the action) and the blocks push the sprinter up and forward with an equal and opposite force (the reaction) - this ground reaction force is what actually propels them. The paired forces act on different bodies, so they never cancel.

The power of the laws is that they are applied together to explain a whole action. Consider a standing vertical jump: by the third law the jumper pushes down on the ground and the ground pushes back up (ground reaction force); by the second law the resultant upward force (reaction minus weight) produces an upward acceleration proportional to that force; and by the first law, once airborne with no upward force acting, the jumper's upward velocity is reduced by gravity until they fall. Analysing a named sporting action through all three laws, and calculating the acceleration with

F = ma

, is the core skill this section rewards.

F = ma

Newton's second law

The resultant force F (newtons) equals mass m (kilograms) multiplied by acceleration a (metres per second squared).

W = mg

Weight

Weight is the gravitational force on a mass; g is about 9.81 m per second squared.

Worked example

Acceleration of a struck ball

A footballer strikes a 0.44 kg ball with a resultant force of 1100 N during contact. Calculate the acceleration of the ball during the kick.

Choose the law
The resultant force and the mass are known and the acceleration is required, so use Newton's second law.
Rearrange
From F = ma, the acceleration is a = F / m.
$a = \dfrac{F}{m} = \dfrac{1100}{0.44}$
Evaluate
1100 divided by 0.44 gives 2500.
$a = 2500\ \text{m s}^{-2}$

Result: The ball accelerates at 2500 m s-2 during contact - a large acceleration because the ball's mass is small and the force is large.

Typical mistakes

Treating a Newton's-third-law pair as cancelling - the action and reaction act on different bodies, so they do not cancel on one body.
Confusing mass and weight in F = ma - use mass in kilograms; weight is the force of gravity (W = mg).

Active revision

A 60 kg sprinter generates a resultant forward force of 480 N from the blocks. Calculate their initial acceleration, and explain the action-reaction forces involved.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

Force, free-body diagrams and ground reaction force#

StandardAQA 7582 3.2.3.1DfE GCE PE - force and free-body diagrams

Force-time graph and impulse

Fig. 2The vertical ground reaction force rises and falls during a foot contact; the shaded area under the curve is the impulse, which equals the change in momentum.

A force is a push or a pull that can change an object's state of motion (its speed, direction or shape); it is a vector, with both magnitude and direction, measured in newtons. The forces acting on a sporting body fall into a few types: weight (the downward gravitational force,

W = mg

); the normal (vertical) reaction force from a surface; friction (which opposes the tendency to slide between two surfaces and is essential for grip and propulsion); and air resistance (a form of drag opposing motion through the air). The net or resultant force is the single force equivalent to the vector sum of all the forces acting.

A free-body diagram represents a single object as a point or box and draws every force acting on it as an arrow, with the length showing the magnitude and the direction showing the line of action. It is the essential first step in any mechanical analysis because it isolates the object and its forces, so that the resultant - and therefore the acceleration, by

F = ma

- can be found. A performer standing still has balanced vertical forces (reaction equals weight) and no horizontal force, so the resultant is zero and they remain at rest.

Ground reaction force (GRF) is the force exerted by the ground on the body in response to the force the body exerts on the ground - a direct application of Newton's third law. It has a vertical component (supporting the body and, in a jump or sprint, propelling it upward) and a horizontal component (providing the backward push against the ground that drives a runner forward, and the braking force as the foot lands). Analysing the size and direction of the GRF explains how a performer generates propulsion and controls landing.

Impulse links force and momentum over time: impulse is the product of force and the time for which it acts,

\text{impulse} = F \times t

, and it equals the change in momentum it produces (

F t = \Delta(mv)

). Because impulse is the area under a force-time graph, a sprinter accelerates by generating a large net forward (propulsive) impulse - the propulsive impulse exceeding the braking impulse over each foot contact - while a performer landing or catching reduces the peak force by increasing the time over which the momentum changes (bending the knees, giving with the hands). Interpreting a force-time graph and relating its area to the change in momentum is a standard higher-level question.

\text{impulse} = F \times t = \Delta(mv)

Impulse-momentum

Impulse (force multiplied by time) equals the change in momentum it produces; it is the area under a force-time graph.

Worked example

Impulse and change in velocity

A 0.16 kg hockey ball is struck and its velocity changes from rest to 30 m s-1. The stick is in contact with the ball for 0.02 s. Calculate the average force applied.

Find the change in momentum
Change in momentum = m(v - u) = 0.16 x (30 - 0) = 4.8 kg m s-1.
Apply the impulse-momentum relationship
Impulse = F x t = change in momentum, so F = change in momentum / t.
$F = \dfrac{\Delta(mv)}{t} = \dfrac{4.8}{0.02}$
Evaluate
4.8 divided by 0.02 gives 240.

Result: The average force applied is 240 N; increasing the contact time (a longer follow-through) would reduce the peak force for the same change in momentum.

Typical mistakes

Including forces the object exerts on other bodies in its free-body diagram - only the forces acting on the object are drawn.
Confusing force with impulse - impulse is force multiplied by the time it acts, and equals the change in momentum.

Active revision

Sketch a free-body diagram of a cyclist travelling at constant velocity on a flat road, and explain what the diagram shows about the resultant force.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

Centre of mass and stability#

StandardAQA 7582 3.2.3.1DfE GCE PE - centre of mass

Stability: line of gravity within the base of support

Fig. 3A body is stable while the line of gravity from the centre of mass falls within the base of support; a lower centre of mass and a wider base increase stability.

The centre of mass is the single point at which the whole mass of a body can be considered to act - the point of balance about which the body's mass is evenly distributed. In a symmetrical object it lies at the geometric centre, but the human body is not rigid: as a performer changes shape, their centre of mass moves, and it can even lie outside the body (as in the arched Fosbury flop, where the high-jumper's centre of mass can pass below the bar while the body passes over it).

The centre of mass governs stability, which also depends on the base of support (the area beneath the body in contact with the ground) and the line of gravity (the vertical line from the centre of mass to the ground). A body is stable and balanced as long as the line of gravity falls within the base of support; it topples when the centre of mass moves so that the line of gravity passes beyond the edge of the base. This single principle explains a great deal of sporting technique.

Four factors determine how stable a position is. A lower centre of mass is more stable (a rugby player crouches low in a scrum); a larger base of support is more stable (a wide stance in a defensive position); the more centrally the line of gravity falls within the base, the more stable the position; and greater mass gives greater stability. A performer manipulates these factors according to whether they want stability or mobility.

The key applied idea is that stability and readiness to move are a trade-off, and skilled performers switch between them. A judoka or a defender adopts a low, wide, stable stance to resist being moved; a sprinter in the 'set' position deliberately raises their centre of mass and moves the line of gravity towards the front of the base, making themselves unstable so that the slightest forward force topples them into a fast start. Analysing why a performer adopts a particular stance - and predicting when they will lose balance - through the position of the centre of mass, the base of support and the line of gravity is exactly what this section tests.

Worked example

Choosing a stance for the task

A rugby player must remain on their feet in a maul, then moments later must accelerate quickly from a jog. Explain how they should manipulate their stability for each demand.

In the maul
To resist being moved, lower the centre of mass, widen the base of support (a wide, crouched stance) and keep the line of gravity central - all four factors maximise stability.
Accelerating away
To move quickly, raise the centre of mass and lean forwards so the line of gravity moves towards the front edge of the base, reducing stability so a small force starts rapid movement.
The trade-off
Stability resists movement, so the player deliberately trades stability for mobility depending on whether they need to hold position or to accelerate.

Result: Low, wide and central for stability in the maul; high and forward for instability and a fast start - stability and mobility are a deliberate trade-off.

Typical mistakes

Assuming the centre of mass is always inside the body - it moves as the body changes shape and can lie outside it (e.g. the Fosbury flop).
Considering only the base of support and ignoring where the line of gravity falls within it.

Active revision

Explain, using the centre of mass, base of support and line of gravity, why a sprinter in the 'set' position is deliberately unstable while a judoka adopts a stable stance.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

Lever systems and mechanical advantage#

AdvancedAQA 7582 3.2.3.1DfE GCE PE - lever systems

The three classes of lever

Fig. 4The class is set by the middle component: first class (fulcrum in the middle), second class (load in the middle, a force advantage), third class (effort in the middle, a speed/range advantage).

The body moves its bony levers about joints, and every lever has three components: the fulcrum (the pivot, at the joint), the effort (the force from the muscle) and the load (the resistance, such as the weight of the body part or an implement). The three classes of lever are defined by which component lies in the middle. In a first-class lever the fulcrum is in the middle (effort-fulcrum-load), as in extension of the elbow by the triceps or the nod of the head at the neck. In a second-class lever the load is in the middle (fulcrum-load-effort), as in plantar-flexion at the ankle when rising onto the toes. In a third-class lever the effort is in the middle (fulcrum-effort-load), as in flexion of the elbow by the biceps - and this is the most common class in the body.

The efficiency of a lever is measured by its mechanical advantage, defined as the ratio of the effort arm to the load arm - the perpendicular distances from the fulcrum to the lines of action of the effort and the load:

MA = \dfrac{\text{effort arm}}{\text{load arm}}

. A mechanical advantage greater than one means the effort arm is longer than the load arm, so a small effort can move a large load - a force advantage. A mechanical advantage less than one means the effort arm is shorter than the load arm, so a large effort is needed to move a smaller load, but the load moves through a larger range and at greater speed.

The class of lever therefore determines its function. Second-class levers always have a mechanical advantage greater than one (the effort arm exceeds the load arm), so they are built for strength - the calf muscles can lift the whole body onto the toes. Third-class levers always have a mechanical advantage less than one (the effort arm is shorter than the load arm), so they sacrifice force for range and speed - the biceps must exert a large force, but the hand at the end of the forearm moves quickly through a wide arc, which is exactly what is needed to throw or strike. First-class levers can have a mechanical advantage greater or less than one, depending on the position of the fulcrum.

Because a lever is in rotational equilibrium when the effort moment equals the load moment (

\text{effort} \times \text{effort arm} = \text{load} \times \text{load arm}

), the short effort arm of a third-class lever explains why muscles must generate such large forces. For a biceps holding a weight, the muscle attaches close to the elbow (a short effort arm) while the weight is at the hand (a long load arm), so the muscle force must be many times the weight - the price paid for the speed and range that make throwing and striking possible. Identifying the lever class in a named action, and calculating its mechanical advantage or the required muscle force from the moments, is the most demanding skill in this chapter.

MA = \dfrac{\text{effort arm}}{\text{load arm}}

Mechanical advantage

The ratio of the effort arm to the load arm; greater than one gives a force advantage, less than one gives a speed/range advantage.

\text{effort} \times \text{effort arm} = \text{load} \times \text{load arm}

Principle of moments (equilibrium)

A lever is balanced when the effort moment equals the load moment about the fulcrum.

Worked example

Mechanical advantage and muscle force in a biceps curl

In a biceps curl the biceps inserts 4 cm (0.04 m) from the elbow and a 50 N dumbbell is held 32 cm (0.32 m) from the elbow. Calculate the mechanical advantage of the lever and the force the biceps must exert to hold the weight.

Identify the lever
The elbow (fulcrum) is at one end, the biceps effort is in the middle and the load is at the hand: a third-class lever.
Mechanical advantage
MA = effort arm / load arm = 0.04 / 0.32.
$MA = \dfrac{0.04}{0.32} = 0.125$
Apply moments for the muscle force
For equilibrium, effort x effort arm = load x load arm, so effort = (50 x 0.32) / 0.04.
$\text{effort} = \dfrac{50 \times 0.32}{0.04} = 400\ \text{N}$
Interpret
The mechanical advantage is less than one, so the biceps must exert 400 N to hold a 50 N weight - the price of the speed and range the arm gains.

Result: The mechanical advantage is 0.125 and the biceps must exert 400 N to hold the 50 N dumbbell - a third-class lever trading force for speed and range.

Typical mistakes

Mixing up the lever classes - remember the middle component: first class = fulcrum, second class = load, third class = effort.
Assuming a low mechanical advantage is 'bad' - third-class levers trade force for the speed and range that throwing and kicking need.

Active revision

For a biceps curl (a third-class lever), the biceps inserts 4 cm from the elbow and holds a dumbbell 32 cm from the elbow. Calculate the mechanical advantage and the muscle force needed to hold a 50 N dumbbell.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

References & sources

Sources

Department for Education

GCE AS and A level subject content for physical education

AQA

AQA A-level Physical Education 7582 specification

Biomechanical Movement

4 sections~17 min reading time3 competenciesLevel Standard 3 · Advanced 1

Biomechanical Movement

Key points

Acceleration of a struck ball

Key points

Impulse and change in velocity

Key points

Choosing a stance for the task

Key points

Mechanical advantage and muscle force in a biceps curl

Sources

Biomechanical Movement

Key points

Acceleration of a struck ball

Key points

Impulse and change in velocity

Key points

Choosing a stance for the task

Key points

Mechanical advantage and muscle force in a biceps curl

Sources