In simple terms
A friendly intro before the formal notes — no formulas yet.
The Physics of Flight and Spin
Biomechanics applies the laws of physics to understand how athletes move. By analysing forces, motion, and energy, we can explain why certain techniques are more effective and how to improve performance.
Think about throwing a frisbee versus a shot put. The frisbee is designed to fly, using air to generate lift, and its flight is very sensitive to spin and angle. The shot put is designed to be a pure projectile, where initial speed and angle are everything, and we try to minimise air resistance. Biomechanics gives us the tools to understand the 'why' behind both.
- 1
Identify the key biomechanical principle at play, such as projectile motion, impulse, or angular momentum.
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Analyse the forces acting on the athlete or object, including gravity, muscle force, friction, and air resistance.
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Apply relevant formulae and concepts to calculate variables like force, velocity, or momentum.
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Evaluate how an athlete could modify their technique to optimise the outcome based on these biomechanical principles.
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step 1
Identify the key biomechanical principle at play, such as projectile motion, impulse, or angular momentum.
Key formulas
Tap any symbol to reveal exactly what it means and its units.
$Impulse = Force (F) × time (t) = Change in momentum (Δp) \ F × t = m(v - u)$
Full topic notes
Formal explanation with the rigour you need for the exam.
Projectile Motion: The Science of Flight
Any object that is thrown, kicked, or hit into the air becomes a projectile. In a vacuum, a projectile follows a perfect parabolic path determined by gravity. However, in sport, we must consider three key factors controlled by the athlete: the speed of release, the height of release relative to the landing surface, and the angle of release. Additionally, external factors like air resistance and spin (Magnus effect) can significantly alter this path.
Speed of Release: The most critical factor. Greater speed results in greater horizontal distance.
Height of Release: A greater release height relative to landing height increases flight time and distance for a given speed and angle.
Angle of Release: The theoretical optimum angle is 45° when release and landing heights are equal. If release height is above landing height (e.g., shot put), the optimal angle is less than 45°. If release height is below landing height (e.g., long jump), the optimal angle is slightly above 45°.
Air Resistance: This force opposes the motion of the projectile, reducing its maximum height and horizontal range, and making the trajectory asymmetrical.
Impulse: The Key to Changing Momentum
To change an object's motion (its momentum), a force must be applied over a period of time. This combination of force and time is called impulse. Athletes manipulate this relationship constantly. To generate maximum velocity, like in a throw or a jump, they apply a large force for the longest possible time. Conversely, to absorb force safely, like when catching a ball, they increase the time over which the force is absorbed, thereby reducing the peak force experienced.
Impulse = Force (F) × time (t) = Change in momentum (Δp) \ F × t = m(v - u)
Coefficient of Restitution (COR): The 'Bounciness' Factor
The Coefficient of Restitution (COR) quantifies the elasticity of a collision. It's a crucial concept in sports involving a ball and a surface or implement, like tennis, golf, or cricket. A COR of 1 represents a perfectly elastic collision with no energy loss, while a COR of 0 represents a perfectly inelastic collision where the objects stick together. In reality, all sporting collisions fall somewhere in between. Factors like the materials of the colliding objects, their temperature, and impact velocity can all affect the COR.
COR =
Angular Motion: The Principles of Spin
Many sports skills involve rotation, from a diver performing a somersault to a figure skater's spin. This is described by angular motion. The key principle is the conservation of angular momentum. Angular momentum is the product of an object's moment of inertia and its angular velocity. The moment of inertia is a measure of how difficult it is to rotate an object, and it depends on mass and how that mass is distributed. By changing their body shape, athletes can alter their moment of inertia and, consequently, their rate of spin (angular velocity).
Angular Momentum (L) = Moment of Inertia (I) × Angular Velocity (ω)
Conservation: If no external torque (turning force) acts on the system, angular momentum (L) is conserved.
Manipulating Spin: An ice skater pulls their arms in to spin faster. This decreases their moment of inertia (I), so their angular velocity (ω) must increase to keep L constant.
Slowing Spin: To slow down or stop a spin, the skater extends their arms and legs. This increases their moment of inertia (I), causing their angular velocity (ω) to decrease.
Application in Diving: A diver leaves the board with a fixed amount of angular momentum. By moving from a layout (high I) to a tuck (low I) position, they dramatically increase their angular velocity to complete multiple somersaults. They then open up again to slow the rotation for a clean entry into the water.
For calculation questions, always write down the formula you are using, show your substitutions, and state your final answer with the correct units. Even if your final calculation is wrong, you can still earn marks for showing the correct method and reasoning.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A rugby player kicks a stationary ball of mass 0.45 kg. The ball leaves the player's foot with a velocity of 25 m·s⁻¹. If the foot was in contact with the ball for 0.07 seconds, calculate the average force exerted on the ball.
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Identify the relevant formula: The impulse-momentum theorem, F × t = m(v - u). We need to find F.
A squash ball is dropped from a height of 2.54 m onto a court surface. It rebounds to a height of 0.85 m. Calculate the coefficient of restitution for the ball-surface interaction.
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Identify the relevant formula: COR = √(rebound height / drop height)
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Try to recall each definition before you reveal it.
Quick check
Answer in your head first — then tap to check. No pressure.
Revision flashcards
Flip the card. Test yourself before the exam.
Projectile Motion
The motion of an object thrown or projected into the air, subject only to the acceleration of gravity (and air resistance). Its path is a parabola in ideal conditions.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
- ✓
Speed of Release: The most critical factor. Greater speed results in greater horizontal distance.
- ✓
Height of Release: A greater release height relative to landing height increases flight time and distance for a given speed and angle.
- ✓
Angle of Release: The theoretical optimum angle is 45° when release and landing heights are equal. If release height is above landing height (e.g., shot put), the optimal angle is less than 45°. If release height is below landing height (e.g., long jump), the optimal angle is slightly above 45°.
- ✓
Air Resistance: This force opposes the motion of the projectile, reducing its maximum height and horizontal range, and making the trajectory asymmetrical.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Test your understanding of biomechanics with these practice questions.
Test your understanding of biomechanics with these practice questions.
Extra simulations & links
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Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do Test your understanding of biomechanics with these practice questions. on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.