EnglandPhysical EducationSyllabus dot point

How is rotation controlled, and what governs the flight path of a projectile in sport?

Angular motion and projectile motion: angular velocity and acceleration, moment of inertia, angular momentum and its conservation, and the factors affecting projectile flight (speed, angle and height of release) and the parabolic path.

A focused answer to Eduqas A-Level PE on angular and projectile motion: the angular quantities, moment of inertia, the conservation of angular momentum applied to spins and somersaults, the three factors affecting projectile flight, and why the optimum release angle is not always 45 degrees, with calculation.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

The angular quantities are angular displacement (radians), angular velocity (rad/s) and angular acceleration. The moment of inertia is the resistance to a change in rotation and depends on the mass and, crucially, how far that mass is from the axis of rotation. Angular momentum is $H = I \times \omega$ (moment of inertia times angular velocity) and is conserved in flight because no external torque acts. So a gymnast tucks to bring mass close to the axis (lowering the moment of inertia, raising angular velocity, spinning faster) and opens out to slow the spin for landing. For a projectile, the horizontal distance depends on the speed, angle and height of release. The optimum angle is 45 degrees only when release and landing heights are equal; a higher release (a shot put) needs less. A projectile follows a parabola when air resistance is negligible.

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What this dot point is asking
The angular quantities and moment of inertia
Conservation of angular momentum
Projectile motion
The parabolic flight path

What this dot point is asking

Eduqas wants you to define the angular quantities and moment of inertia, explain the conservation of angular momentum and apply it to spins and somersaults, and explain the factors affecting projectile flight, including why 45 degrees is not always the optimum angle.

The angular quantities and moment of inertia

Conservation of angular momentum

Projectile motion

The parabolic flight path

For a dense object (a shot, a discus) air resistance is negligible, so the only force in flight is weight acting downward. The horizontal velocity stays constant (no horizontal force) while the vertical velocity changes uniformly under gravity (decreasing on the way up, increasing on the way down), giving a symmetrical parabola. For a light object with a large surface area (a shuttlecock, a beach ball), air resistance is significant and distorts the path, so the flight is non-parabolic, falling more steeply at the end.

Using the conservation of angular momentum in a dive

Write the relationship

Use angular momentum $H = I \times \omega$ , and recall that $H$ is conserved in flight because no external torque acts.

State the value at take-off

Suppose a diver leaves the board in a layout (open) position with a moment of inertia of $15$ kg m squared and an angular velocity of $4$ rad/s, so $H = 15 \times 4 = 60$ kg m squared rad/s.

Apply the tuck

The diver tucks, halving the moment of inertia to about $7.5$ kg m squared. Because $H$ is conserved at $60$ , the new angular velocity is $\omega = \frac{H}{I} = \frac{60}{7.5} = 8$ rad/s, so the spin doubles in speed, allowing more rotations.

Open out to land

Before entry the diver opens out, raising the moment of inertia back toward $15$ kg m squared, so $\omega$ falls back to about $4$ rad/s for a controlled, near-vertical entry. State that the diver never changes $H$ ; they only trade $I$ against $\omega$ .

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20183 marksA diver has a moment of inertia of 12 kg m squared and an angular velocity of 5 rad/s. Calculate their angular momentum, give the unit, and state whether it changes once they leave the board.

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A Component 1 angular calculation. One mark for the value, one for the unit, one for the conservation point.

Use angular momentum $H = I \times \omega$ , so $H = 12 \times 5 = 60$ kg m squared rad/s. Once the diver leaves the board, no external torque acts (only gravity through the centre of mass), so angular momentum is conserved: it stays at 60 kg m squared rad/s throughout the flight. The diver can change their angular velocity by changing their moment of inertia (tucking or opening out), but the product stays constant.

A common dropped mark is saying angular momentum changes in flight; it is conserved, while moment of inertia and angular velocity trade off.

Eduqas 20226 marksExplain the three factors that affect the horizontal distance of a projectile, and explain why a shot putter releases at less than 45 degrees while a long jumper takes off at around 20 degrees.

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A Component 1 projectile question. Markers reward the three factors and the two applied explanations.

Award marks for: the horizontal distance of a projectile depends on the speed of release (the greater the release velocity, the further it travels, and this is the most important factor), the angle of release, and the height of release. The optimum angle is exactly 45 degrees only when the release height equals the landing height. A shot putter releases the shot from above shoulder height, so the release is higher than the landing; the extra height already adds flight time, so the optimum release angle drops below 45 degrees (around 37 to 42 degrees). A long jumper's priority is to keep a high horizontal velocity from the run-up, and raising the take-off angle toward 45 degrees would cost too much horizontal speed, so the effective take-off angle is much lower, around 20 degrees, trading some height for the speed that carries them forward.

A top answer ranks release speed as the dominant factor and links the release height to why the angle falls below 45 degrees.

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Sources & how we know this

Eduqas A Level Physical Education Specification — Eduqas (2016)