Motion and forces

Before explaining why things move, describe how. Displacement is change in position and has direction; distance is path length and does not. Velocity is rate of change of displacement; speed is rate of change of distance. Acceleration is rate of change of velocity, which means changing direction at constant speed is still acceleration.

Graphs carry a lot of this. On a displacement-time graph the gradient is velocity. On a velocity-time graph the gradient is acceleration and the area beneath is displacement. Reading a question as a graph is often faster than reaching for an equation.

The first law says an object keeps its velocity unless a resultant force acts. It defines what a force does: forces change motion, they do not maintain it. A crate sliding to a halt is not evidence against this, it is evidence of friction.

The second law says resultant force equals mass times acceleration. Note resultant: it is the vector sum that matters, so a body with many forces in balance behaves exactly like one with no forces at all. The third law says forces come in pairs that are equal, opposite, and act on different bodies. That last clause is the one students miss, and it is why an action and reaction pair never cancel each other out.

• Weight: mass times gravitational field strength, always directed toward the centre of the planet.
• Normal force: the perpendicular push of a surface, adjusting itself to prevent objects sinking through.
• Friction: opposes relative sliding; static friction can exceed kinetic friction, which is why things are harder to start than to keep moving.
• Tension: the pull transmitted along a rope or cable.
• Drag: resistance through a fluid, growing with speed, which is what produces terminal velocity.

Momentum is mass times velocity, and in any isolated system the total is conserved. This turns collisions into bookkeeping: total momentum before equals total momentum after, regardless of what happens during the impact.

Collisions are elastic when kinetic energy is also conserved and inelastic when some becomes heat, sound or deformation. Impulse, force times the time it acts, equals the change in momentum, which explains airbags and crumple zones: extending the collision time reduces the peak force for the same momentum change.

• Draw the situation and mark every force as an arrow on the body itself.
• Choose a positive direction and stay with it for the whole problem.
• Resolve forces into components along and perpendicular to the motion.
• Apply the second law along the direction of acceleration, and set the perpendicular direction to balance.
• Check that the answer has sensible units and a plausible size before moving on.