Dynamics: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 3 · Read time: ~10 minutes
Key Formulas
Newton's laws in terms of momentum
Newton's First Law: an object's momentum stays constant unless a resultant force acts on it.
Newton's Second Law (general form): the resultant force on an object equals its rate of change of momentum, F = Δp/Δt. This is the more fundamental statement of the law, F = ma is only the special case where mass doesn't change.
Newton's Third Law: unchanged from O Level, when object A exerts a force on object B, B exerts an equal and opposite force back on A, same type of force, acting on two different objects, simultaneously.
Trap: F = ma only works when mass is constant. For a system where mass itself changes during the motion (e.g. a rocket burning fuel, rain filling an open truck), you must use the general momentum form, since expanding Δ(mv) then involves a term from the changing mass as well as the changing velocity.
Impulse and force-time graphs
Impulse equals the change in momentum it produces: J = FΔt for a constant force, or the area under a force-time graph for a force that varies with time.
Real-world application: for a given impulse (a fixed change in momentum, e.g. stopping a falling object), extending the contact time reduces the peak force involved. This is why crumple zones, airbags, and 'giving' with your hands when catching a ball all work, they spread the same impulse over a longer time, lowering the peak force on the object or person.
Trick: For an irregularly-shaped force-time graph, estimate the area the same way you would for a velocity-time displacement question, split it into simple shapes (or count squares) rather than searching for a single formula that fits the whole curve.
Collisions: elastic vs inelastic
Momentum is always conserved in a collision, provided no external resultant force acts on the system, this is true regardless of what type of collision it is.
An elastic collision conserves both momentum AND total kinetic energy. An inelastic collision conserves momentum but NOT total kinetic energy, some KE is converted to heat, sound, or deformation. A perfectly inelastic collision is the special case where the objects stick together afterwards.
To classify a collision, calculate total KE before and total KE after separately, then compare them, don't assume from the description alone.
Trap: Kinetic energy is a scalar, so when calculating ½mv² for each object, use its actual speed, not a signed velocity that might be negative. Signed (positive/negative) velocities are essential for momentum, but irrelevant once you're squaring for kinetic energy.
Worked Example
Trolley P, of mass 2.0 kg, moves at 6.0 m/s to the right and collides with stationary trolley Q, of mass 4.0 kg. After the collision, trolley P moves at 2.0 m/s to the left.
(a) Calculate the velocity of trolley Q immediately after the collision. [3]
Taking rightward as positive: mP uP + mQ uQ = mP vP + mQ vQ
(2.0 × 6.0) + (4.0 × 0) = (2.0 × −2.0) + (4.0 × vQ)
12.0 = −4.0 + 4.0 vQ
vQ = 4.0 m/s to the right
(b) Calculate the total kinetic energy of the system before and after the collision. [3]
KE before = ½(2.0)(6.0)² + 0 = 36.0 J
KE after = ½(2.0)(2.0)² + ½(4.0)(4.0)²
= 4.0 + 32.0 = 36.0 J
(c) State, with a reason, whether this collision is elastic or inelastic. [1]
Total KE before (36.0 J) equals total KE after (36.0 J),
so the collision is elastic.
Why this question is a good test of the topic: trolley P bouncing backward can look 'inelastic' on intuition alone, but the only valid test is comparing total kinetic energy before and after, which here turns out to be conserved exactly.
Frequently Asked Questions
What's the general form of Newton's Second Law?
F = rate of change of momentum (Δp/Δt). It reduces to F = ma only when the object's mass is constant.
What is impulse and how do I find it from a graph?
Impulse equals the change in momentum produced, which equals the area under a force-time graph.
What's the difference between elastic and inelastic collisions?
An elastic collision conserves both momentum and kinetic energy. An inelastic collision conserves momentum only, some kinetic energy is converted to heat, sound, or deformation.
Is momentum always conserved in a collision?
Yes, as long as no external resultant force acts on the system, for both elastic and inelastic collisions.
Which paper is this tested in?
Paper 1 MCQs often test impulse-from-graph and Newton's Third Law concepts. Paper 2 and Paper 3 typically include a full momentum/collision calculation similar to the worked example above.
Momentum and collisions calculations not clicking?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, taught by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author.