Dynamics: Complete O Level Physics Cheatsheet

Newton's three laws of motion

Newton's First Law: An object stays at rest, or moves at constant velocity in a straight line, unless a resultant (net) force acts on it. In other words, an object's motion only changes if the forces on it are unbalanced.

Newton's Second Law: The resultant force on an object equals its mass times its acceleration: F = ma. A bigger resultant force produces a bigger acceleration; a bigger mass, for the same force, produces a smaller acceleration.

Newton's Third Law: Whenever object A exerts a force on object B, object B exerts an equal and opposite force back on object A. These two forces are always the same type (e.g. both gravitational, or both contact forces), act on different objects, and act simultaneously.

Trick: To correctly identify a Newton's Third Law pair, check all three conditions at once: same type of force, equal magnitude, opposite direction, acting on two *different* objects. A book resting on a table has two forces on it (its weight, and the table's normal reaction), but these are NOT a Third Law pair, they act on the *same* object (the book) and are usually different types of force that happen to balance. The book's weight's actual Third Law pair is the force the book exerts back on the Earth.

Trap: Students often think a resultant force is needed to keep something moving at constant velocity. It isn't, by the First Law, zero resultant force means constant velocity (which includes staying at rest), not that the object slows down. A car moving at constant speed on a level road has zero resultant force, since the driving force is exactly balanced by resistive forces (friction, air resistance).

F = ma in practice

F = ma uses the resultant force. If multiple forces act on an object, find the resultant (net) force first, usually by adding forces in the same direction and subtracting forces in the opposite direction, before applying F = ma.

Weight is itself a force: W = mg, where g is the gravitational field strength (approximately 10 N/kg near the Earth's surface, at O Level).

Rearranged forms are just as testable: a = F/m (for finding acceleration) and m = F/a (for finding mass).

Trap: Don't confuse mass and weight when applying F = ma. Mass (kg) goes directly into the equation; if a question gives you weight instead, you first need m = W/g to find the mass.

Momentum and conservation of momentum

Momentum (p = mv) describes how much 'motion' a moving object has, combining both its mass and its velocity.

Principle of Conservation of Momentum: in a collision (or explosion) where no external resultant force acts, the total momentum of the system just before equals the total momentum just after. This holds true whether the collision is elastic (objects bounce apart) or inelastic (objects stick together).

Working with direction: since momentum is a vector, you must define a positive direction first. An object moving in the negative direction has negative momentum, this matters when adding momenta together in a collision question.

Trick: For a 'stick together' (perfectly inelastic) collision, treat the two objects as one combined mass moving at one common final velocity: m₁u₁ + m₂u₂ = (m₁ + m₂)v. This single-equation shortcut only works when the objects end up moving together, check the question says they stick/couple together before using it.

Worked Example

Trolley A, of mass 2.0 kg, moves at 3.0 m/s to the right and collides with stationary trolley B, of mass 1.0 kg. After the collision, the two trolleys stick together and move off as one.

Why this question is a good test of the topic: part (b) only works because the two trolleys stick together, that's what justifies treating them as one combined mass. Part (c) then shows the same collision from a force perspective, using force = change in momentum ÷ time rather than F = ma directly, since trolley A's velocity changes over a measurable time.

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