Biomechanical principles: motion (linear, angular), force, momentum, levers, projectile motion, Newton's laws of motion, the application of biomechanics to improving performance

What this dot point is asking

QCAA wants you to know the core biomechanical principles (linear and angular motion, force, momentum and impulse, lever systems, projectile motion, and Newton's three laws) and then apply them to a specific movement in a chosen physical activity to explain or improve performance. The science is only worth marks when it is tied to a real sporting action with correct terminology and units.

The answer

Linear and angular motion

Linear motion is movement in a straight line. A 100 m sprinter's centre of mass moves linearly down the track. Angular motion is movement around an axis. A gymnast doing a somersault rotates around their centre of mass, and a discus thrower rotates around their longitudinal axis before release.

Most sporting movements combine both. A long jumper has angular motion in the legs during the run-up and takeoff, linear motion of the centre of mass through the flight phase, and further angular motion (the hitch-kick) in the air.

Newton's three laws of motion

These are the foundational principles.

First law (inertia). An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net force. A stationary soccer ball stays put until it is kicked. A sprinter at the blocks does not move until they apply force to the blocks.

Second law (force, mass, acceleration). Acceleration is proportional to net force and inversely proportional to mass.

A heavier rugby player needs more force to accelerate than a lighter player. The relationship between applied force and resulting acceleration sets the athlete's power output.

Third law (action and reaction). For every action there is an equal and opposite reaction. A swimmer pushes water backwards and the water pushes the swimmer forwards. A high jumper presses down on the ground and the ground reaction force lifts them. Action and reaction is the basis of all locomotion.

Force

Force is a push or a pull that changes motion, measured in newtons (N). Key force concepts in sport:

• Net force. The sum of all forces on an object. If forces balance, net force is zero and there is no acceleration.
• Friction. Opposes motion at a surface contact. Sport demands different friction, from high friction at sprint spike points to low friction under a curling stone.
• Air resistance (drag). Opposes motion through air. It matters for cyclists, runners and ski jumpers, and drives aerodynamic equipment design.
• Ground reaction force. The force the ground exerts back on an athlete who pushes down, measurable with a force plate.
• Buoyancy. The upward force water exerts on a submerged body, central to swimming.

Momentum and impulse

Momentum is mass times velocity.

A 100 kg rugby player moving at 5 m/s has a momentum of 500 kg m/s. Impulse is force applied over time, and impulse equals the change in momentum.

To produce a large change in momentum you can apply a large force for a short time, a smaller force for a longer time, or both. A javelin thrower's long pull applies force over a longer arm path, producing larger impulse and greater release velocity. A landing gymnast bends the knees to extend the time over which force is absorbed, reducing the peak force on bones and joints.

Levers

The body is a system of levers, with bones as lever arms and joints as fulcrums.

• First-class lever. Fulcrum between effort and load, for example the head balancing on the neck (atlanto-occipital joint as fulcrum).
• Second-class lever. Load between fulcrum and effort, for example a standing calf raise (ball of foot as fulcrum, body weight as load).
• Third-class lever. Effort between fulcrum and load, for example a biceps curl (elbow as fulcrum, biceps as effort). Most human joints work as third-class levers.

Third-class levers trade force for speed and range. The biceps must produce more force than the weight being lifted, but the hand moves further and faster than the muscle contracts, which is useful for throwing and striking.

Projectile motion

A projectile in flight is acted on by gravity (downward) and air resistance (opposing motion). Three factors set the flight:

• Speed of release. Higher release speed gives a longer flight, and range scales with the square of release speed.
• Angle of release. For maximum horizontal distance from and to the same height, 45 degrees is optimal. When release is above the landing surface the optimal angle drops, so a shot put is released at around 38 to 42 degrees.
• Height of release. A higher release point extends flight time and therefore distance.

A long jumper uses around 18 to 22 degrees because forward velocity matters more than maximising vertical lift, while a basketball free throw uses a steep angle near 50 degrees to drop into the hoop.

Application to improving performance

Biomechanics earns marks when it is used to make athletes faster, stronger or more skilled. Coaches use force plates and high-speed video to analyse sprint ground reaction force, swimming stroke mechanics, throwing release parameters, and gymnastics angular velocity, then change technique or equipment to remove the limiting factor.

Examples in context

Example 1. AFL set shot for goal. The kick is a third-class lever action at the knee, the boot applies an impulse to the ball, and the ball then becomes a projectile. To reach a long goal from 50 m, the player generates a high release speed through a long, fast kicking leg (large impulse) and chooses an angle around 30 to 40 degrees to balance distance against the available time in the air. Newton's third law applies at the plant foot, where the ground reaction force stabilises and drives the kick.

Example 2. Track sprinter at the Queensland State Championships. Out of the blocks the athlete applies a large backward and downward force; the block reaction force (third law) drives them forward, and the resulting acceleration follows the second law (more horizontal force per kilogram of body mass means more acceleration). Through the race the centre of mass moves linearly while the limbs move angularly about the hip, knee and ankle. Force plate data lets a coach target the weakest phase, often the first two steps.

Try this

Q1. Define impulse and explain, using a gymnast landing from a vault, how increasing impulse time reduces the risk of injury. [3 marks]

• Cue. Impulse = force times time and equals change in momentum. The gymnast must reduce momentum to zero on landing, so bending the knees extends the time, which lowers the peak force on bones and joints for the same change in momentum.

Q2. A discus thrower wants to increase throwing distance. Using projectile motion principles, explain two changes that would increase range and justify each. [4 marks]

• Cue. Increase release speed (range scales with the square of speed, so this has the greatest effect) by a faster rotation across the circle; release nearer the optimal angle for an above-ground release (around 35 to 40 degrees) so velocity is split efficiently between horizontal travel and flight time.

Q3. Identify the lever class operating at the elbow during a biceps curl, label the fulcrum, effort and load, and explain the trade-off this lever provides. [4 marks]

• Cue. Third-class lever; fulcrum at the elbow, effort from the biceps, load is the weight in the hand. Trade-off: the muscle must produce more force than the load, but the hand gains speed and range of movement, which benefits throwing and striking.