Newton's Laws of Motion

A body stays at rest, or keeps moving in a straight line at constant speed, until an external force acts on it. That reluctance to change state is inertia, and it depends only on mass: more mass, more inertia.

• Passengers lurch forward when a bus brakes because their bodies keep the original motion
• A dusting cloth removes dust because the cloth moves while the dust resists
• Seat belts exist to supply the external force your body needs in a crash

Key point: no change of motion happens without an external force, so "constant velocity" means the forces balance to zero.

The acceleration of a body is directly proportional to the resultant force, inversely proportional to its mass, and points in the force's direction. One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².

The calculation pattern

1. List the forces and find the resultant
2. Apply F = ma to get the acceleration
3. Use kinematics if the question asks for velocity or distance

A 2 kg mass pushed with 10 N against friction of 2 N accelerates at (10 - 2) / 2 = 4 m/s². Examiners hide the second force (friction, tension or weight), so always subtract before you divide.

Key point: resultant force first, then F = ma. Never divide the raw push by the mass.

For every action there is an equal and opposite reaction: equal in size, opposite in direction, acting on different bodies. That last phrase is the trap: because the two forces act on different objects, they never cancel each other.

• A gun recoils as the bullet leaves; the rocket rises by pushing gas down
• Walking works because you push the ground backward and the ground pushes you forward
• Swimming, rowing and jet propulsion are all third-law engines

Momentum is mass times velocity, and the second law can be rewritten as "force equals rate of change of momentum". In collisions where no external force acts, total momentum is conserved, the bookkeeping that makes crash and explosion questions solvable.

• Before = after: m1u1 + m2u2 = m1v1 + m2v2
• An explosion starts from rest, so the fragments' momenta cancel in pairs