Laws of Motion

Topic-by-topic explanations

1. Introduction

Newtonian mechanics explains how forces change motion. Before using a law, identify the object or system and choose axes.

2. Aristotle's fallacy

Aristotle's fallacy arises from everyday friction: objects usually need a push to keep moving because resistance slows them. Without a net force, motion continues at constant velocity.

3. The law of inertia

Inertia is resistance to a change in motion. Mass measures translational inertia. Newton's first law states that an object remains at rest or in uniform straight-line motion unless acted on by a non-zero resultant external force.

4. Newton's first law of motion

Newton's first law defines inertial frames and the zero-net-force case. A body can move while its resultant force is zero; force is needed to change velocity, not to sustain constant velocity.

5. Newton's second law of motion

Newton's second law is ΣF=dp/dt. For constant mass, ΣF=ma, with acceleration in the direction of the resultant force.

6. Newton's third law of motion

Newton's third law says interaction forces are equal in magnitude, opposite in direction and act on different bodies. They do not cancel each other on a single free-body diagram.

7. Conservation of momentum

Momentum is p=mv. When net external impulse is zero, total momentum of a system is conserved. Impulse J=Δp; lengthening stopping time reduces average force for a fixed momentum change.

8. Equilibrium of a particle

A particle is in translational equilibrium when ΣFₓ=0 and ΣFᵧ=0. Draw the force diagram, resolve components and solve simultaneous equations if needed.

9. Common forces in mechanics

Weight acts vertically downward; normal force is perpendicular to a contact; tension acts along a taut string; friction resists relative sliding or its tendency. Static friction adjusts up to μₛN; kinetic friction is approximately μₖN.

10. Circular motion

Circular motion requires inward resultant force ΣFᵣ=mv²/r. The required centripetal force is supplied by real forces such as tension, gravity or friction; it is not an extra force.

11. Solving problems in mechanics

Good mechanics problem-solving starts with a diagram, a choice of system and axes, known/unknown quantities, a law, algebraic solution, unit check and physical check.

Formula sheet

Use consistent SI units, identify the system and assumptions, and show the steps of each calculation. Check units and whether the result is physically reasonable.

Worked example

Common errors and revision checklist

Never draw action-reaction forces on the same object's diagram. Static friction is not always μN. Use the net radial force for circular motion.

• Write the relevant law or relation before substituting values.
• Show units, signs and directions.
• Check assumptions and round only the final result.