Bio-mechanics

Newton's 1st law: Law of inertia

• Object will remain at rest/uniform velocity unless acted upon by an external/unbalanced force.
• Greater the mass, greater the inertia (inertia-resistance of body to change its state).
• e.g. sprinter will remain in blocks until an external force large enough to overcome their inertia creates motion OR they continue at constant velocity unless acted upon by an external force.

Newton's 2nd law of motion: Law of acceleration

• Body's rate of change in momentum is proportional to the size of force applied and acts in the same direction as the force applied (force= mass x acceleration).
• Mass is constant therfore to generate a large force, greater acceleration must be applied.
• E.g. greater the force applied to the sprinter, greater the rate of change in momentum and therefore greater acceleration from blocks.

Newton's 3rd law of motion: Law of reaction

• For every action applied to a body there is an equal and opposite reaction.
• E.g. when the sprinter applies a down/backwards force into the blocks, blocks apply equal and opposite up/forward force to drive sprinter forward out the blocks.

Velocity

• Rate of change in displacement (shortest straight line route between start/finish).
• Velocity (m/s) = displacement (m) / time taken (s).

Momentum

• Quantity of motion possessed by a moving body.
• Momentum (kgm/s) = mass (kg) x velocity (m/s).

Acceleration

• Rate of change in velocity.
• Acceleration (m/s/s) = (final velocity - initial velocity m/s) / time taken (s).

Force

• A push or pull that alters the state of motion of a body.
• Force (N) = mass (kg) x acceleration (m/s/s)

Force and its effects 

• Push/pull that alters state of motion of a body: can be internal (skeletal muscle) or external.
• Has 5 effects: motion, acceleration, deceleration, change direction, change shape.
• If the net force is 0, object remains stationary or constant velocity.
• If ground reaction force is greater than weight, body travels upwards (high jump).
• Net force: sum of all forces acting on body (0= no change as forces are balanced, constant velocity or rest), if there's a net force then forces are unbalanced so has an effect.

Vertical forces

• Weight: gravitational pull that earth exerts on a body (acts downwards from COM).
• Weight (N) = mass (kg) x acceleration due to gravity (m/s/s)
• Reaction: equal and opposite reaction force exerted in response to action force.
• Reaction force is always present when 2 bodies are in contact.

Force and its effects 

• Push/pull that alters state of motion of a body: can be internal (skeletal muscle) or external.
• Has 5 effects: motion, acceleration, deceleration, change direction, change shape.
• If the net force is 0, object remains stationary or constant velocity.
• If ground reaction force is greater than weight, body travels upwards (high jump).
• Net force: sum of all forces acting on body (0= no change as forces are balanced, constant velocity or rest), if there's a net force then forces are unbalanced so has an effect.

Vertical forces

• Weight: gravitational pull that earth exerts on a body (acts downwards from COM).
• Weight (N) = mass (kg) x acceleration due to gravity (m/s/s)
• Reaction: equal and opposite reaction force exerted in response to action force.
• Reaction force is always present when 2 bodies are in contact.

Horizontal forces

• Friction: force that opposes the motion of 2 surfaces in contact (friction can be increased by: roughness of ground or contact surface, temp, size of normal reaction).
• Air resistance: force opposing motion of a body travelling through the air (affected by: velocity, shape, frontal cross-sectional area, smooth surface).

Free-body diagram

• Shows where the net force originates, the size of the force and direction it's acting in.
• Can consider the net force and the resultant force that occurs= motion.

Limb kinematics 

• Kinematics: study of movement in relation to time/space.
• Evaluates joint/limb efficiency by measuring bone geometry, displacement, velocity and acceleration in planes of movement (adjust technique)
• Infra-red camera captures motion on reflective markers (2D model)
• Highly specialised, expensive and limited to labs.

Force plates

• GRF measured (asses size/diretion of force, acceleration rate, work/power output).
• Used for gait analysis, balance, rebab, analyse performance and health (e.g. WiiFit).

Wind tunnels

• Used by trailing cars to develop drag-reduction systems by decreasing drag up to 7%.
• Cycle helmets/F1 cars can be tested for aerodynamic efficiency: wind tunnel streamlines its path through the air and increases lift/decreases drag.
• Wind tunnels allow you to manipulate environmental variables.

Centre of mass

• Point at which a body's mass is balanced evenly in all directions.
• Can be manipulated to improve technique (raise arms to raise COM), can move outside the body and act as a point of rotation (somersault= moves COM in front of body, rotates around).
• Flight path of COM is predermined at take-off.

Stability

• Ability of body to resist motion/remain at rest (withstand force and return to position, balanced).
• Factors affecting it: mass, height (lower the COM, greater stabiltity), base of support, line of grabity (more central to base of support, greater stability).

Maximising stability

• Sprinter in blocks has max stability: low COM, large base of support (5 points of gravity), line of gravity falls within base of support, high mass.

Minimising stability

• Set is called: raise hips to raise COM, lifts knee (reduce base of support), leans forward (shift line of gravity).
• Instability is maximised as gun is fired: chest lifts raising COM, hands off track (minimise base of support), line of gravity falls in front of base of support so drive forwards.

Levers 

• 4 components: lever (bone) fulcrum (joint), effort (muscular force), load (resistance/weight).
• Bones act as levers around a fixed point (fulcrum). When a muscle contracts, effort is created.
• 1, 2, 3 : F, L E. (most are 3rd class e.g. elbow flexion).
• First class (elbow extension e.g. holding javelin), second class (plantar flexion at take-off).

Efficiency of lever system 

• Effort arm: distance from fulcrum to effort.
• Load arm: distance from fulcrum to load.
• Greater this distance, more significant the effort or load.
• Longer levers generate greater force as load arm lengthens and accelerates more (tennis ball).
• 2nd and 3rd class have mechanical disadvantage: effort arm is greater than load arm so need a larger effort to move a small load (operates at knee joint during extension to kick ball).
• 1st class has mechanical advantae as load arm is smaller than effort arm, moves a large load with little effort, e.g. at foot to vertically accelerate body.

Linear motion

• Movement of a body in a straight/curved line where all parts move the same distance in the same direction over the same time (water skier on flat lake at constant speed).
• Due to a direct force applied through COM.
• Descriptors: distance, displacement (e.g. in 100m sprint it's 100m), speed, velocity, acceleration and deceleration.

Graphs of linear motion 

• Distance/time: gradient indicates speed at certain instant/rest/constant speed/acceleration or deceleration (gradient is change in y/change in x axis).
• Speed/time: gradient shows acceleration and whether its rest/constant/acceleration/deceleration.
• Velocity/time: gradient shows acceleration at certain instant/rest/uniform velocity/acceleration/deceleration.

Angular motion

• Movement of a body/bodypart in a circular path about an axis of rotation.
• Results from an eccentric force being applied outside the body's COM (e.g. toque).

Principal axes of rotation

• Is an imaginary line passing through COM about which a performer can rotate:
• Longitudinal: head to toe through COM e.g. flat spin on ice/full turn in trampolining.
• Transverse: left to right through COM e.g. somersault.
• Frontal: front to back through COM e.g. cartwheel.

Principal axes of rotation and planes of movement 

• Sagittal about frontix axis: flexion like squatting, walking, extension with overhead press.
• Frontal about transverse axis: abduction like star jump, side bend like adduction.
• Transverse about longitudinal axis: rotation like throwing, pronation like bowling.

Angular motion key descriptors 

• Angular velocity: rate of change in displacement or rate of rotation.
• Angular velocity (rad/s) = angular displacement (rad) / time taken (s).
• Moment of inertia: resistance of body to change state of angular motion.
• Moment of inertia (kgm2) = sum of (mass x distribution of mass from axis of rotation).
• Greater the mass, greater the MOI (raise arms above head).
• If MOI is high, resistance to rotation is high so angular velocity is low- slow rate of spin.
• Angular momentum: quantity of angular motion possessed by a body.
• Angular momentum (kgm2rad/s) = MOI (kgm2) x angular velocity (rad/s).
• Eccentric force creates angular momentum: angular momentum determines speed of rotation.
• Once it's generated, its a product of MOI and angular velocity: inversely proportional.

Conservation of Angular momentum

• A rotating body will continue to turn about its axis of rotation with constant angular momentum unless acted upon by an eccentric force/torque.
• Can't be changed in flight so generate as much as possible in take-off (manipulate MOI/velocity by twists, turns, spins).

Fluid mechanics

• Forces acting on a body travelling through air/water (air resistance in air, drag in water).
• Both must be minimised to maximise performance.

Factors affecting the magnitude of air resistance and drag

• Velocity: greater it is, greater the air resistance/drag. Cannot be reduced however.
• Frontal cross-sectional area: larger it is, larger air resistance/drag. e.g. cyclist tries to reduce.
• Streamlining/shape: more aerodynamic/streamlined body, lower drag. More aerodynamic the equipment is, lower it is e.g. tear drop helmet.
• Surface characteristics: smoother the surface, lower it is (tight lycra clothing to reduce friction between fluis and the body surface).
• Downhill skiing must generate large momentum/high velocity so must battle air resistance: low crouched position to minimise air resistance, tear-drop helmet to streamline and lyra for smooth surface.
• Cyclists minimise air resistance: lightweight carbon fibre bike with aerodynamic disc wheels to minimise air resistance, aerodynamic position to reduce frontal cross-sectional area.

Projectile motion

• Movement of a body through the air following a curved flight path under gravity.
• Projectile: body launched into the air and subjected to weight/air resistance.
• Once in flight a projectile follows flight path: shows overall distance travelled after gravity has accelerated it back to the ground surface.

Projectile release

• Parabola: symmetrical flight path, downward vertical acceleration, weight is dominant force.
• Non-parabolic: non-symmetrical flight path, air resistance is dominant.
• Affected by: speed of release (faster velocity, more distance), angle of release (45 is opt e.g. long jump, 45+ for golf, -45 for shot-put), height of release (45 is opt if release/landing height are equal).
• E.g. in the javelin, the opt angle of release is -45 as the projectile already has an increased flight time due to increased height of release.

Projectiles in flight 

Flight path

• Once released, projectile follows flight path determined by size of forces acting upon it.
• If weight is dominant, parabolic flight path e.g. shot put has high mass/low velocity with small frontal-cross sectional area so air resistance is negligable.
• If air resistance is dominant, non-parabolic flight path e.g. badminton shuttle has low mass/high velocity with uneven surface which increases air resistance.

Free body diagrams

• Shows forces acting on projectile in flight: size, direction, net force, motion and flight path.
• 3 phases of motion in a flight path to highest point after which gravity will accelerate projectile to the ground: start, mid and end of flight.
• Air resistance will be greater at start after release as it's travelling with highest velocity.

Parallelogram of forces

• Shows forces acting on projectile and resultant force: if the resultant force is closer to weight arrow, weight is dominant (parabolic), if closer to air resistance (non parabolic).
  

Bernoulli principle 

• Creation of an additional lift force on a projecile in flight resulting from Bernoulli's conclusion that the higher the velocity of air flow, the lower the pressure.
• Lift increases flight path and horizontal distance covered= makes it non-parabolic.
• E.g. ski jumper is aerofoil shape with curved upper surface and flat underneath: air travels at a higher velocity over the curved surface and at a low velocity underneath as it's a shorter distance.
• As velocity increases, pressure decreases- curved zone is low pressure: fluids move from high to low so pressure gradient forms creating an additional lift force.

Downward lift force

• Happens with inverted aerofoils: e.g. Formula 1/track cycling to increase downward force that holds them to the track at high speed around corners.
• Formula 1: front wing funnels and spoiler bar act as inverted aerofoils, forcing air underneath to travel a further distance at higher velocity with low pressure).
• Pressure gradient creates additional downward lift force.

Magnus force

• A force created from a pressure gradient on opposing surfaces of a spinning body in the air.
• Magnus effect: creation of additional Magnus force on a spinning projectile which deviates from the flight path.
• Spin made by applying an external force outside COM.
• Magnus effect works for Bernoulli: pressure gradient formed either side of spinning projectile and an additional magnus force is creates deviating the flight path to non-patabolic.

Spin

• 1: Topspin- eccentric force applied above COM (spins downwards around transverse axis).
• 2: Backspin- eccentric force applied through COM (spins left around longitudinal axis).
• 3: Sidespin hook- eccentric force through COM (spins left around longitudinal axis).
• 4: Sidespin slice- eccentric force applied left of COM (spins right around longitudinal axis).
• Topspin rotation creates downward magnus force, shorterning flight path (attack shot).
• Backspin rotation creates upward magnus force, lengthening flight path (defensive shot).
• Sidespin rotation creates magnus force to right (slice) and left (hook), swerving the projectile right (slice) and left for a hook.

Ball with topsin: additional force is created by-

• Upper surface of projectile rotating towards oncoming air, which opposes motion, decreasing velocity of air flow= high pressure.
• Lower surface of projectile rotating in same direction as air, increases velocity of air and creates low pressure zone.
• Pressure gradient forms and additional magnus force created downwards.
• Downward magnus force adds to weight of the projectile and effect of gravity is increased.
• Projectile dips in flight so flight path shortens.
• Use of topspin shortens flight path so can hit it harder (can confuse opposition in tennis by bringing them closer to the net).