Newton’s laws of motion

· Newton’s laws of motion explain how forces cause or change movement in sport and exercise.
· Linear motion = movement in a straight or curved path where the whole body/object moves together, e.g. sprinting, cycling, a ball travelling forwards.
· Angular motion = rotation around an axis, e.g. a gymnast somersaulting, a diver rotating, a discus spinning.
· Motion can be described using speed, velocity and acceleration.
· The resultant motion of an object depends on the sum of all forces acting on it.
· Key exam idea: movement changes only when there is a resultant/unbalanced force.

Newton’s first law: inertia

· Law of inertia: a body remains at rest or continues moving with constant velocity unless acted on by a resultant external force.
· Inertia = resistance to a change in motion; greater mass = greater inertia.
· Sporting examples:
· A sprinter needs a large force against the blocks to overcome inertia.
· A heavy athlete/object is harder to accelerate or stop.
· A ball stays still until kicked, thrown or hit.
· Exam phrase: no resultant force = no change in velocity.

Newton’s second law: force, mass and acceleration

· Acceleration depends on the resultant force and the mass of the body/object.
· Formula from the data booklet: force = $F = ma$.
· Greater force produces greater acceleration if mass is constant.
· Greater mass produces less acceleration if force is constant.
· Sporting examples:
· A stronger push against the ground increases sprint acceleration.
· A lighter ball accelerates more than a heavier ball when the same force is applied.
· Increasing force production improves jumping, throwing and striking performance.
· Weight is a force caused by gravity: $W = mg$.

Newton’s third law: action–reaction forces

· For every action force, there is an equal and opposite reaction force.
· These forces act on different bodies, not the same body.
· Sporting examples:
· A runner pushes backward and downward on the ground; the ground reaction force pushes the runner forward and upward.
· A swimmer pushes water backwards; water pushes the swimmer forwards.
· A jumper pushes down on the ground; the ground pushes up to launch the body.
· Exam phrase: performance improves when athletes apply force in the correct direction to create an effective reaction force.

Stability

· Stability = ability to resist being moved or toppled.
· Stability increases when:
· centre of mass is lower
· base of support is larger
· line of gravity falls within the base of support
· line of gravity is more central within the base of support
· mass is greater
· Sporting examples:
· Rugby players lower their body position and widen their stance before contact.
· Gymnasts need controlled centre of mass over the base of support when landing.
· Wrestlers and judo athletes lower their centre of mass to resist being thrown.

Stability is improved by lowering the centre of mass and widening the base of support. A performer is most stable when the line of gravity remains within the base of support. Source

Summing joint forces

· Summing joint forces = sequential use of body segments to produce a larger final force or velocity.
· Usually occurs from large, slow, proximal segments to smaller, faster, distal segments.
· Effective summation requires:
· correct timing
· correct sequence
· stable body position
· transfer of momentum through linked segments
· Sporting examples:
· Throwing: legs → hips → trunk → shoulder → elbow → wrist → fingers.
· Kicking: hip → knee → ankle → foot.
· Tennis serve: legs → trunk → shoulder → arm → racket.
· Exam phrase: poor timing reduces force transfer and lowers performance.

Linear motion, impulse and momentum

· Linear momentum = quantity of motion in a straight-line direction.
· Formula from the data booklet: $p = mv$.
· Impulse = force applied over time; impulse changes momentum.
· Key relationship: greater impulse = greater change in linear momentum.
· Increase impulse by:
· applying a larger force
· applying force for a longer time
· applying force in the correct direction
· Sporting examples:
· Longer contact time in a jump take-off can increase impulse.
· Follow-through in striking helps apply force for longer.
· Bending knees on landing increases stopping time and reduces peak force.
· The principle of impulse direction means the direction of the applied impulse determines the direction of the momentum change.

Impulse depends on both force and contact time. In sport, athletes manipulate impulse to increase speed, change direction or reduce impact forces during landing. Source

Angular motion and eccentric force

· Angular motion = rotation around an axis.
· Angular motion is produced when a force acts at a distance from the centre of mass.
· This off-centre force is called an eccentric force.
· The further the force acts from the centre of mass, the greater the tendency to rotate.
· Sporting examples:
· A diver creates rotation at take-off by applying force away from the centre of mass.
· A gymnast generates angular motion during a somersault.
· A ball hit off-centre may spin.
· Exam phrase: eccentric force produces rotation.

Conservation of angular momentum

· Angular momentum is conserved when an athlete or object is free from additional eccentric forces.
· In flight, angular momentum usually remains constant because there is little external torque.
· Athletes can change angular velocity by changing body shape:
· tucked position = smaller moment of inertia → faster rotation
· extended position = larger moment of inertia → slower rotation
· Sporting examples:
· Divers tuck to rotate faster and extend to slow before entry.
· Figure skaters pull arms in to spin faster.
· Gymnasts alter body shape to control rotation in flight.

The skater spins faster when the arms are pulled in because the moment of inertia decreases. Angular momentum is conserved when external torque is negligible. Source

Key equations from the SEHS data booklet

· Speed = distance ÷ time.
· Linear velocity = displacement ÷ time.
· Angular velocity = angular displacement ÷ time.
· Acceleration = change in velocity ÷ time.
· Linear momentum = $p = mv$.
· Force = $F = ma$.
· Weight = $W = mg$.
· Assessment note: trigonometry is not assessed.
· Calculation limit: SL = up to three terms, HL = up to four terms.

Friction acts parallel to the contact surface and opposes motion or attempted motion. In sport, friction can improve grip, acceleration and control, but excessive friction can reduce efficiency. Source

Checklist: can you do this?

· Apply Newton’s three laws to explain sporting movements such as sprinting, jumping, throwing, swimming and landing.
· Explain stability using centre of mass, base of support, line of gravity and mass.
· Use impulse and momentum to explain changes in speed, direction and impact force.
· Distinguish linear and angular motion, including how eccentric force creates rotation.
· For HL, interpret collisions, coefficient of restitution, friction, work and power in sporting contexts.