AS Physics: Dynamics, Newton Laws and Momentum — Revision Notes

Condensed for the final weeks. For the full explanation, use the Dynamics study guide.

Newton’s laws

First law — an object stays at rest or moves at constant velocity unless acted on by a resultant force.

Second law — the rate of change of momentum is proportional to the resultant force and occurs in its direction:

F = delta-p / delta-t      which reduces to  F = ma  only when mass is constant

Stating the second law as F = ma is incomplete. The momentum form is the general one, and it is required for problems involving changing mass, such as sand falling onto a conveyor. Caution with a rocket burning fuel: naively differentiating F = Δ(mv)/Δt using only the rocket’s own changing mass and velocity is a common mistake, because it omits the momentum carried away by the ejected exhaust gas — the thrust actually depends on the rate at which mass is ejected and the exhaust’s velocity relative to the rocket, found by applying conservation of momentum to the rocket-plus-exhaust system, not by differentiating the rocket’s momentum alone. Acceleration and resultant force always act in the same direction — a useful check when resolving forces in more than one dimension.

Third law — for every force there is an equal and opposite force. The pair must act on two different bodies and be of the same type. Weight and normal contact force on a book are not a third-law pair — they act on the same body.

Weight is not mass. Weight = mg is the gravitational force on a mass, and depends on the local gravitational field; mass is constant wherever the object is.

Non-uniform motion and terminal velocity

Without air resistance, a falling object accelerates uniformly at g. With air resistance present, drag increases as speed increases, so the resultant force — and therefore the acceleration — decreases as the object speeds up. Eventually drag equals weight, resultant force is zero, and the object falls at a constant terminal velocity.

Momentum and impulse

p = mv                    kg m s^-1
impulse = F t = delta-p   N s

Impulse is the area under a force–time graph.

This explains safety features directly: a crumple zone, airbag or crash mat increases the time over which a given momentum change occurs, so by F = Δp/Δt the average force is reduced. For the standard exam scenario — comparing the same collision (same initial and final speeds) with and without the safety feature — the momentum change is unchanged and only the time varies; this is a simplification, since real crumple zones and airbags can also affect the rebound and final speed of the occupants, not just the collision time, but “longer time, same Δp, smaller force” is the relationship you are expected to apply. Answers that say the airbag “absorbs the force” score nothing.

Conservation of momentum

In a closed system with no external resultant force, total momentum before = total momentum after.

Momentum is a vector — assign a positive direction and treat opposite motion as negative. This is the single biggest source of lost marks in collision calculations.

Collision	Momentum	Kinetic energy
Elastic	Conserved	Conserved
Inelastic	Conserved	Not conserved
Perfectly inelastic	Conserved	Not conserved; objects stick together

Momentum is always conserved; kinetic energy is not. In an inelastic collision the “lost” kinetic energy becomes thermal energy, sound and deformation — it is not destroyed.

For a perfectly elastic collision, relative speed of approach equals relative speed of separation.

Explosions

Momentum before is zero, so momentum after must total zero — the fragments move in opposite directions with equal and opposite momenta. Kinetic energy increases, supplied by chemical or elastic potential energy.

Worked example. A 2.0 kg trolley moving at 3.0 m s⁻¹ collides with a stationary 1.0 kg trolley and they stick together. By conservation of momentum: (2.0 × 3.0) + (1.0 × 0) = (2.0 + 1.0)v, so v = 2.0 m s⁻¹. KE before = ½ × 2.0 × 3.0² = 9.0 J; KE after = ½ × 3.0 × 2.0² = 6.0 J — the 3.0 J difference is lost to heat and sound, confirming a perfectly inelastic collision.

Exam traps

• Quoting F = ma as Newton’s second law without the momentum form.
• Identifying weight and normal contact force as a third-law pair.
• Ignoring the vector nature of momentum in a collision.
• Saying kinetic energy is conserved in all collisions.
• Explaining an airbag as “absorbing force” rather than extending the time.
• Forgetting that the resultant force is what matters in the first law.

Self-test

1. State Newton’s second law properly, and say when F = ma is valid.
2. Give the two conditions for a third-law force pair.
3. How does a crumple zone reduce the force in a crash?
4. Which quantity is conserved in all collisions, and which is not?
5. What happens to the “lost” kinetic energy in an inelastic collision?
6. Explain why a falling skydiver eventually reaches a constant velocity.
7. Distinguish between weight and mass.

Answers: 1. The rate of change of momentum is proportional to the resultant force and acts in its direction; F = ma follows only when mass is constant. 2. The two forces act on different bodies and are of the same type. 3. It increases the time over which the momentum change occurs, and since force equals rate of change of momentum, a longer time gives a smaller force. 4. Momentum is always conserved; kinetic energy is conserved only in elastic collisions. 5. It is transferred to thermal energy, sound and the work done deforming the objects. 6. As speed increases, air resistance (drag) increases, reducing the resultant force and acceleration, until drag equals weight and the resultant force is zero — the object then falls at a constant terminal velocity. 7. Weight is the gravitational force on a mass (weight = mg) and depends on the local gravitational field; mass is the amount of matter in an object and is constant everywhere.