amazon.co.ukA-level PE biomechanics revision: Newton's laws applied to sport, levers and mechanical advantage, linear and angular motion, projectile release factors, fluid mechanics (Bernoulli and Magnus), impulse and force-time graphs, centre of mass and stability for AQA 7582, OCR H555 and Edexcel 9PE0.
Newton's laws underpin every biomechanics explanation. First law (inertia): a body stays at rest or moves at constant velocity until an external force acts - a sprinter remains motionless in the blocks until the applied force exceeds inertia; a heavier rugby player has more inertia and is harder to stop or start. Second law: the acceleration of a body is proportional to the force applied and inversely proportional to its mass - F = ma (force in newtons, mass in kg, acceleration in m/s squared); a netball pass accelerates more when more force is applied over the ball's small mass. Third law: for every action there is an equal and opposite reaction - the sprinter pushes back and down on the blocks and the blocks push forward and up on the sprinter; a swimmer pushes water backwards and is propelled forwards; a ball is struck with a force equal and opposite to the force the ball applies to the racket. Exam logic: state the law in full, then give one precise sporting example - the marks are for the application, not the recitation.
Levers consist of a fulcrum (pivot), load (weight/resistance) and effort (force applied by the muscle). First class: fulcrum between load and effort - nodding the head (atlanto-occipital joint as fulcrum, head weight as load, neck muscles as effort) or triceps extension at the elbow. Second class: load between fulcrum and effort - plantar flexion/heel raise (ball of the foot is the fulcrum, body weight through the ankle is the load, calf muscles through the Achilles are the effort); second-class levers always give mechanical advantage (effort moves a larger load with less force) but a small range and slow movement. Third class: effort between fulcrum and load - biceps curl (elbow fulcrum, biceps insertion effort, weight in hand load) and most limb movements (knee extension, elbow flexion); third-class levers operate at a mechanical disadvantage (large effort needed for a small load) but produce great speed and range of movement - the classic trade-off the exam wants. Mechanical advantage = effort arm / load arm (distance from fulcrum to effort versus fulcrum to load). Application: most sporting limbs are third class because speed of racket, boot or fist matters more than economy of force - hence biceps and quadriceps insert close to the joint.
Linear motion is movement of the body (or parts) in a straight or curved line where all parts move the same distance, direction and speed in the same time. Distinguish the pairs precisely: distance (path length, scalar) versus displacement (straight-line change of position from start to finish, vector - a 400 m runner on one lap has 400 m distance but zero displacement); speed (distance/time, scalar) versus velocity (displacement/time, vector with direction, m/s); acceleration = change in velocity / time taken (m/s squared). Momentum = mass x velocity (kg m/s): the quantity of motion a body possesses; in a collision (tackle) momentum is conserved in the combined bodies unless an external force acts - a heavier, faster player has more momentum and is harder to stop. Impulse = force x time: impulse changes momentum - the greater the impulse, the greater the change in velocity. Applications score the marks: increasing time of contact reduces peak force (a cricketer or netball player draws the hands back when catching - cushioning; landing with bent knees spreads the force); increasing force and/or time increases momentum change (a long jumper drives hard through a long last-contact; a discus thrower's long pull; follow-through in striking actions). Impulse also explains negative impulse (braking forces in the early stance of running - the first half of ground contact decelerates, the second accelerates).
Force-time graphs link directly to impulse: the area under the curve = impulse. Exam graphs typically show ground reaction forces in sprinting or landing: identify the peak force, explain that the same impulse can be generated by a smaller force acting for longer (why good landings look soft), and note the negative (braking) and positive (propulsive) phases of the running contact. In jump analysis, a larger area under the vertical force-time curve means a greater take-off impulse and therefore greater take-off velocity and jump height.
Worked calculations - the exam sets numericals, so rehearse the four: (1) Force: a 75 kg sprinter accelerating at 4 m/s squared produces F = 75 x 4 = 300 N; (2) Momentum: an 80 kg player moving at 8 m/s has momentum of 80 x 8 = 640 kg m/s; in a tackle the combined mass moves with the conserved momentum of the pair; (3) Velocity: 100 m covered in 12.5 s gives velocity = 100 / 12.5 = 8 m/s (state the direction for the vector mark); (4) Impulse: an average force of 200 N applied for 0.25 s gives impulse = 200 x 0.25 = 50 Ns, the change in momentum produced. Show units in every calculation - missing units is the most common lost mark.
Friction completes the force picture: static friction acts between surfaces at rest and is essential in sport - sprint blocks, football studs and climbing shoes all rely on static friction to create the grip that makes the third-law reaction force possible (a boot slipping on wet grass produces no useful reaction); kinetic friction acts between moving surfaces and is usually resistive - skiers wax bases and cyclists use narrow, smooth-rolling tyres to cut it. Friction can therefore be necessary or resistive depending on the task - a discrimination point: athletes want maximum friction at the shoe-surface interface (grip) and minimum friction at the body-fluid interface (streamlined suits). Combine with drag: both are resistive forces the performer manipulates - the exam rewards naming the force, stating its direction, and explaining the performer's manipulation of it. For impulse numericals on force-time graphs, remember the area under the curve method: estimate the area of each rectangle/triangle region and sum it - that area is the impulse and hence the momentum change.
Distance, displacement and the games application - the worked example that scores: a 400 m runner on a standard track runs a distance of 400 m but a displacement of zero (start and finish coincide) - the classic discrimination; velocity can therefore be zero while speed is high, and velocity can be negative (deceleration, or motion in the opposite direction - a defender back-pedalling). Acceleration is positive when speeding up, negative when slowing down (deceleration in the run-up), and zero at constant velocity (top-speed sprinting between 60-80 m in a 100 m race) - quote one of each in linear motion answers. In games, displacement matters more than distance: a midfielder's total distance covered (10+ km) is quantitative workload, but the displacement of a pass (straight-line direction and length) determines whether it reaches the intended receiver - the vector qualities (direction + magnitude) are what the exam rewards.
Lever dimensions in the body - the numbers behind mechanical disadvantage: in a knee extension (third-class lever), the patellar tendon inserts roughly 4-5 cm from the knee joint (effort arm) while the load (lower leg plus any resistance) acts roughly 30-40 cm from the joint (load arm) - the quadriceps must generate roughly 8-10 times the load force to extend the knee, but the foot travels 8-10 times faster and further than the muscle shortens. This is the complete trade-off sentence the exam wants: third-class levers sacrifice force economy for speed and range - hence the body's design for rapid limb movement (kicking, throwing) rather than lifting heavy loads. Second-class levers invert it: the heel raise moves the whole body weight with a calf force well below body weight, but the heel lifts only a few centimetres - force economy at the cost of range. Application: weight-lifting movements that load third-class joints (biceps curl) feel heavy because the muscle works at a mechanical disadvantage - the reason muscles are so strong relative to the loads they move.
Exam logic: define the quantity, give the equation, then apply to the named performer - e.g. impulse questions reward time-force trade-offs in both directions (cushion a catch, lengthen a throw). For levers, always identify fulcrum-load-effort in order, name the class, then state the mechanical advantage consequence.
Angular motion is rotation of a body or segment around an axis (real or imaginary). It is produced by torque (moment of force) = force x perpendicular distance from the axis to the line of action of the force (newton metres) - the further the force acts from the axis, the greater the rotation produced, which is why gymnasts swing long levers. Angular equivalents mirror linear quantities: angular displacement (angle turned, radians or degrees), angular velocity (angle turned per unit time, rad/s), angular acceleration (change in angular velocity per unit time).
Moment of inertia (I) is the resistance of a rotating body to a change in its angular motion: I = sum of (m x r squared) - the sum of each particle's mass times the square of its distance from the axis. Two implications the exam always wants: (1) it depends on mass and, critically, its distribution - the same mass held further from the axis gives a much larger moment of inertia (r is squared); (2) because r is squared, changing body shape (tucking) changes I dramatically without changing mass.
Angular momentum = moment of inertia x angular velocity. When a performer is airborne there is no external torque, so angular momentum is conserved (constant) - it can only be redistributed between I and angular velocity. This is the core principle of aerial sports: take-off determines total angular momentum; shape changes then trade it. Tucking pulls mass towards the axis, decreasing I, so angular velocity must increase - faster somersault. Extending for the landing increases I, so angular velocity decreases - slower rotation, controlled landing. Applications: a trampolinist or diver generating a strong pike/tuck to complete multiple somersaults then extending to land; an ice skater spinning faster as the arms are drawn in; a gymnast in a straight somersault rotating slower than in a tucked one. Note for precision: the performer cannot add angular momentum in the air - only vary its distribution - a discrimination point in evaluate questions.
Projectile motion: any body released into the air and subject only to gravity and air resistance follows a curved (parabolic) path. Three factors affecting the trajectory, in order of importance: (1) speed of release (the greater the release velocity, the further and faster the projectile travels - the dominant factor, which is why force production and technique focus on it); (2) angle of release; (3) height of release (relative to landing height). For release and landing at the same level, the optimum angle is 45 degrees - equal horizontal and vertical velocity components give maximum range. When the projectile is released above landing height (shot put, javelin, ski jump), the optimum angle is less than 45 degrees - elite shot putters release at roughly 36-38 degrees because the extra release height means less vertical component is needed. When released below landing height (e.g. a chip over a keeper), the optimum is greater than 45 degrees. Horizontal and vertical components are independent: horizontal velocity stays (approximately) constant; vertical velocity changes under gravity - quote this for A* precision when explaining why a projectile's shape is a parabola and why maximum range is not always at 45 degrees in real sport (air resistance shifts it for a javelin or badminton shuttle).
Applications to rehearse: long jump (optimum angle ~18-22 degrees in practice because speed cannot be fully converted - a realistic evaluation point), shot put (release height and velocity dominate), golf drive and football punt (angle-speed trade-offs), ski jump (using aerodynamics to extend flight - links to fluid mechanics). Exam logic: state the three factors in the correct order of influence, give the 45 degree rule with its modification for release height, and finish with a performer-specific justification.
Angular calculations and units: angles are measured in radians or degrees; 1 radian is approximately 57.3 degrees and a full turn is 2 x pi radians (approximately 360 degrees). Angular velocity = angle turned / time: a gymnast completing a full 360-degree somersault in 0.5 s turns at approximately 12.6 rad/s (6.28 / 0.5). Worked moment-of-inertia logic: if a performer tucks and reduces I to a third of its extended value, angular velocity must triple (momentum conserved: halving or thirding I multiplies angular velocity by the same factor) - quote this inverse proportionality in numerical questions; converting to a pike position reduces I less than a tuck, so angular velocity rises less - know the shape hierarchy: straight (largest I, slowest rotation), pike (intermediate), tuck (smallest I, fastest rotation).
Real-sport release angles - the applied detail that separates A* answers: long jump - optimum in practice is only ~18-22 degrees because the take-off leg cannot convert all horizontal speed into vertical velocity without destroying run-up speed; speed of release dominates, so elite long jumpers trade angle for velocity - a textbook evaluation of the 45-degree rule. Shot put - ~36-38 degrees, below 45 because the shot is released above landing height (less vertical component needed). Javelin - released at ~30-35 degrees with a small angle of attack (angle between the implement and the airflow) so the aerofoil shape generates lift that extends flight; air resistance makes the flight path asymmetric rather than a true parabola. Ski jumping - the jumper leans forward over the skis to maximise lift and minimise drag, extending the flight far beyond a ballistic path. Exam logic: for projectile questions, state the three factors in order of influence, give the 45-degree rule and its release-height modification, then finish with the real-sport justification - the marks are for explaining why the optimum shifts, not for reciting 45 degrees.
Torque calculations and take-off generation: torque = force x perpendicular distance - a gymnast applying 500 N at 0.4 m from the hip axis generates 200 Nm of torque; the same force at 0.2 m generates only 100 Nm - the reason long levers (straight legs, extended arms) and wide grips generate more rotation. Generating angular momentum at take-off is the detail the conservation questions assume: the performer creates torque while still in contact with the ground - by asymmetric arm actions (one arm up, one down), a lean at contact (trampolinist contacting the bed off-centre), or a hyperextended take-off position (diver's hurdle step) - and the reaction force then supplies the rotation; once airborne, no new torque can be added, only redistributed. State both halves: contact-phase torque generation, then airborne conservation - the two-phase logic that full-mark angular answers follow.
Linear and angular combine in most sporting movements - the synthesis the exam rewards: running is angular rotation of the limbs (hip, knee, ankle) producing linear motion of the centre of mass; a throw combines angular rotation of the trunk and arm (increasing the speed of the distal end through the kinetic chain) with linear drive of the legs; a golf swing is angular motion of the body around the spine axis imparting linear velocity to the club head. The general rule: angular velocity of a rotating limb produces linear velocity of its end point proportional to the radius (v = omega x r) - a longer lever moving at the same angular velocity gives the end point greater linear speed, which is why throwing implements (javelin, hammer) are held at the end of extended arms. Quote one combined example per biomechanics answer - the examiners reward linking the two motion types rather than treating them in isolation.
Drag is the resistance opposing motion through air or water. Two types, both nameable for a mark: surface drag (friction between the fluid and the surface of the body - reduced by smooth skinsuits and shaving legs in swimming/cycling) and form drag (resistance created by the shape and cross-sectional area presented to the flow - reduced by streamlining: the cyclist's crouched aero position, the swimmer's horizontal body line, the bobsleigh's shape). Drag increases with the square of velocity (doubling speed quadruples drag - why aerodynamics matter most at elite speeds), with cross-sectional area, and with less streamlined shape. Application: sprint cyclists adopt an aero tuck and use disc wheels; swimmers wear textured suits to cut surface drag while keeping the body flat to cut form drag; a sprinter deliberately does not streamline (upright running posture) because generating force matters more than reducing drag at those speeds - a strong discrimination point.
The Bernoulli principle: where fluid velocity is higher, pressure is lower. An aerofoil shape (curved upper surface creating a longer path) forces air to travel faster over the top, lowering pressure above relative to below - the pressure differential produces lift perpendicular to the flow. Applications: the discus held at a slight negative angle of attack experiences lift, extending flight; a ski jumper spreads the skis and leans forward, creating lift that prolongs the flight phase; downhill skiers and F1 cars use inverted aerofoils to create downforce (grip). Exam logic: name Bernoulli, state the velocity-pressure inverse relationship, identify the aerofoil/pressure differential and the direction of the resulting force.
The Magnus effect applies Bernoulli to spinning balls - a guaranteed explain question. When a ball is struck with spin, the spinning surface drags a thin boundary layer of air around with it. On the side where the surface moves with the airflow, local air velocity increases and pressure falls (Bernoulli); on the opposite side the surface moves against the airflow, velocity falls and pressure rises. The pressure differential creates a force perpendicular to the flight path, deviating the ball. Direction of spin determines direction of force: topspin produces a downward force so the ball dips early (tennis topspin, a dipping football free kick) but bounces forward; backspin produces an upward force so the ball floats (golf wedge shots, a chip that stops); sidespin swerves the ball left or right (banana free kick). Applications to rehearse: Cristiano Ronaldo's knuckleball-free-kick contrast (minimal spin = unpredictable - optional depth), tennis topspin allowing higher net clearance with the ball still dropping in, golf dimples reducing surface drag to enhance the spin-lift interaction.
Centre of mass is the point at which the body's mass is concentrated and about which it balances - in an upright standing human roughly behind the navel, but it moves as body position changes and can lie outside the body: in the Fosbury flop the arched back places the centre of mass below the bar while the body clears it - a guaranteed application. In a sprint start the centre of mass is low and forward over the hands (facilitating horizontal propulsion); in a high jump take-off it is driven upward.
Stability (resistance to disturbance of equilibrium) is maximised by four factors, a guaranteed 4-mark list: (1) greater body mass; (2) larger base of support (feet apart, multiple contact points); (3) lower centre of mass (crouch); (4) line of gravity falling within the base of support (and more stability when the line is central). Applications: a gymnast landing bends the knees (lowers COM, enlarges base), plants feet apart and holds arms out; a rugby prop in the scrum crouches with a wide stance so the line of gravity stays central; a sprinter in the blocks is deliberately unstable forward - instability can be desirable when fast movement is needed - the balance-versus-readiness trade-off is a top-band evaluation point. Static stability also improves when the performer is stationary and symmetrical; dynamic balance during movement is maintained by adjustments keeping the line of gravity within the moving base.
Buoyancy and flotation (Archimedes' principle) extend fluid mechanics to water: upthrust equals the weight of fluid displaced, so a body floats when its density is lower than water. The swimmer's centre of buoyancy (centre of the displaced water, near the chest/air-filled lungs) sits above the centre of mass (hips and legs, denser muscle and bone), so the body rotates until the two align - the legs sink and the swimmer kicks to raise them, keeping the body horizontal to minimise form drag. Water is roughly 800 times denser than air, so drag dominates swimming: technique, streamlining and the reduced bow-wave all matter more than in land sports - the reason swimming has the highest technique-to-strength ratio of any sport and why shaving down and skinsuits cut surface drag. Applications: front-crawl body roll reduces the cross-sectional area presented; streamlining off the push-off (long, narrow, arms locked) exploits minimal form drag; the breaststroke glide positions the body in the lowest-drag shape.
| Sport | Principle | Application |
|---|---|---|
| Sprint cycling | Form drag / streamlining | Aero tuck, disc wheels, skinsuit - minimises the cross-section presented |
| Swimming | Surface + form drag; buoyancy | Horizontal body line, shaved skin; kick raises legs to align centre of buoyancy with centre of mass |
| Discus | Bernoulli lift | Slight negative angle of attack generates lift, extending flight |
| Ski jumping | Bernoulli lift + drag | Forward lean over skis maximises lift, prolonging flight |
| Football free kick | Magnus effect | Sidespin creates pressure differential, swerving the ball |
| Tennis / golf | Magnus effect | Topspin dips the ball early; backspin floats it |
| Gymnastics landing | Stability + impulse | Wide base, low centre of mass; knee flexion extends contact time, reducing peak force |
Dynamic balance is the final stability depth: in movement the base of support constantly changes, so balance is maintained by keeping the line of gravity within the moving base through postural adjustment - a sprinter leans forward with the centre of mass deliberately ahead of the base at the drive phase (controlled instability converting into horizontal propulsion), then brings the line of gravity back over the feet at top speed. The exam rewards the trade-off framing: stability is desirable for landing and contact sports; instability is deliberately engineered for acceleration and change of direction - quote one example of each.
Exam logic: fluid questions want the named principle (Bernoulli/Magnus), the velocity-pressure relationship and the performer-specific consequence; stability questions want all four factors plus an applied performer; centre-of-mass questions want the Fosbury flop point. For force-time graphs, always state that the area under the curve equals impulse and link it to momentum change.