This unit is ≈4% of the A-Level Physics, across 8 lessons. Full syllabus
Lesson 6 of 8 · Options and board-specific extensions
The physics of sports
8 min read · about 55 min with practice3 quick checks<1% of the testCore: Core: tested on most papers
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This is Option C for Eduqas (Component 3, Section B) and WJEC (Unit 4, Section B). It is worth 20 marks (about 25 minutes), usually set as one or two long structured questions. They open with a definition, work through two or three calculations and often finish with an explanation. Every mark comes from a small set of equations applied to sport, which makes this one of the most dependable places on the paper to score full marks.
By the end you’ll be able to
Apply moments of inertia and conservation of angular momentum to diving, gymnastics and skating
Use the coefficient of restitution and momentum to analyse impacts (bat–ball, bouncing balls)
Explain the Magnus effect and Bernoulli’s principle in swing and spin
Analyse stability and centre of mass in sporting postures
What the exam asks
Stability: use the centre of gravity (CoG) and the base of support to explain toppling, and find a toppling angle.
Moments: muscle forces in the forearm or leg, and a sailor hiking out.
Impulse and restitution:Ft=mv−mu; e=, and for bounces.
vii.Check your understanding
3 questions on the physics of sports. Every option is explained once you answer.
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PromptCard 1 of 3
When does a body topple?
relative speed before
relative speed after
e=h/H
Rotation: moment of inertia, α=tω2−ω1, τ=Iα, L=Iω, conservation of angular momentum, and 21Iω2.
Energy: linear and rotational kinetic energy, for example a ball rolling down a slope.
Projectiles, Bernoulli and drag: projectiles in sport, p=p0−21ρv2 (spin and swing) and FD=21ρv.
Core ideas
Stability and toppling
A body is stable while the vertical line through its CoG falls inside its base. If it tilts, the weight gives a restoring moment. Once that line passes the pivot edge, the moment turns the body further over and it topples. With the CoG at height h above the middle of a base of width b:
tanθtopple=hb/2
A lower CoG and a wider base both increase the angle, which is why wrestlers crouch with their feet apart. A sprinter in the “set” position moves the CoG close to the front edge of the base on purpose, so that almost no force is needed to start falling forward into the run.
Moments in muscles and sailing
In equilibrium the moments about any point balance and the resultant force is zero. The biceps attaches about 4 cm from the elbow, but the hand is about 33 cm away, so the muscle force is many times the load. This mechanical disadvantage buys speed and range: a small contraction produces a large movement of the hand. A sailor hikes out to move their weight further from the pivot, which increases the righting moment that balances the wind’s heeling moment on the sail.
Impulse and restitution
The impulse of the resultant force equals the change in momentum, Ft=mv−mu. Choose a positive direction first. When a ball rebounds, u and v have opposite signs, so the speeds add. Following through increases the contact time, so the same force produces a bigger change in momentum. Landing mats and bent knees increase the stopping time, which reduces the force.
e=relative speed before collisionrelative speed after collision,0≤e≤1
For a ball dropped onto a fixed floor, u=2gH and v=2gh, so e=Hh. Each bounce multiplies the height by e2, and a graph of h against H has gradient e2.
Rotational dynamics
The moment of inertia measures how hard it is to change a body’s rotation. It depends on the mass and on how far that mass is from the axis:
Conservation of angular momentum: with no external torque, I1ω1=I2ω2. A skater or diver who pulls in their limbs reduces I, so ω increases. The kinetic energy 2IL2increases, and the extra energy comes from the work done by the muscles. In flight, the diver’s weight acts through the CoG, so it exerts no torque about it and L stays constant.
Energy with rolling
Rolling without slipping means v=rω, and mgh=21mv2+21Iω2. For a solid sphere this gives 107mv2, so v=10gh/7. For a thin shell it gives 65mv2. Mass and radius cancel, so a solid ball always beats a hollow one down the same slope. Elastic potential energy, 21kx2 (a trampoline or pole vault), fits into the same energy balance.
Projectiles, Bernoulli and drag
The horizontal velocity stays constant, while the vertical motion follows s=uyt−21gt2. When the landing point is below the release point (shot put, long jump), solve the quadratic and take the positive root.
Bernoulli: where air moves faster relative to the ball, its pressure is lower.
p=p0−21ρv2⇒Δp=21ρ(vfast2−vslow
Magnus effect: a spinning ball drags air round with it. On the side where the surface moves with the airflow past the ball, the air is faster and the pressure lower, so the ball is pushed towards that side. Backspin lifts a golf ball, topspin makes a tennis ball dip, and sidespin bends a free kick.
Drag:FD=21ρv2ACD. Terminal velocity is vt=ρACD, and the power needed against drag is P=FDv∝v3.
Worked examples
Exam technique
Write the equation you are using first. Many option marks are method marks, for example “use of L=Iω”.
Revolutions or radians: a ratio of spin rates can stay in rev s⁻¹, but energy, torque and α need rad s⁻¹ (multiply rev s⁻¹ by 2π).
Impulse: mark the positive direction on the page before substituting.
Explain questions need the full chain. For spin: relative air speed, then pressure (Bernoulli), then pressure difference, then the direction of the force. For stability: where the weight’s line of action falls relative to the base, then the moment.
Rolling: state “rolls without slipping, so v=rω”. It is often a mark on its own.
Common mistakes
Quick recap
A body topples when its weight’s line of action falls outside the base; tanθ=hb/2.
For muscles, take moments about the joint, then use the resultant force to find the joint reaction.
Ft=mv−mu with signs; e=approach speedseparation speed, and e=h/H.
I=∑mr2: 52 for a solid sphere and for a thin shell; and .
With no external torque, I1ω1=I2ω, and the KE changes by the factor .
Rolling: mgh=21mv2+ with .
Fast air means low pressure (backspin lifts, topspin dips); FD=21ρv, and drag power .