§ 3.1 Momentum and Newton's laws of motion
Key ideas
- First law: an object stays at rest or moves at constant velocity unless a resultant force acts.
- Second law: the resultant force equals the rate of change of momentum, F = Δp/Δt; for constant mass this reduces to F = ma.
- Third law: if A exerts a force on B, B exerts an equal and opposite force of the same type on A.
- Linear momentum p = mv is a vector along the velocity. Mass measures inertia; weight W = mg is the gravitational force on it.
Equations
p = m vmomentum = mass × velocitykg m s⁻¹
F = Δp / Δtthe general second law; F = ma when mass is constantN
W = m gweight = mass × acceleration of free fallN
Watch out: third-law pairs act on different bodies, are equal in magnitude, opposite in direction, and of the same type. They can never cancel, because they never act on the same object.
§ 3.2 Non-uniform motion
Key ideas
- Drag opposes motion and grows with speed; friction and viscous forces behave the same way.
- For a falling object: at release drag is zero so a = g; as speed rises drag grows, the resultant force shrinks, and the acceleration falls.
- Terminal velocity: when drag has grown to equal the weight, the resultant force and acceleration are zero and the velocity stays constant.
Fig. 1 · The fall starts at gradient g; as drag builds, the curve flattens and the velocity approaches, but never quite crosses, the terminal value.
Watch out: at terminal velocity the acceleration is zero, not the velocity; the object is moving at its fastest. "Forces balanced" never means "stopped".
§ 3.3 Linear momentum and its conservation
Key ideas
- Principle of conservation of momentum: for a system with no external resultant force, the total momentum is constant.
- Elastic collision: kinetic energy is also conserved, and the relative speed of approach equals the relative speed of separation.
- Inelastic collision: momentum is conserved but kinetic energy is transferred to other forms; if the bodies stick together, the collision is perfectly inelastic.
Equations
m1u1 + m2u2 = m1v1 + m2v2total momentum before = total momentum afterkg m s⁻¹
Fig. 2 · An elastic collision checked three ways: momentum and kinetic energy are both conserved, and the relative speed of approach equals the relative speed of separation.
Watch out: momentum is conserved in every collision; kinetic energy only in elastic ones. Never test "momentum conservation" by comparing kinetic energies.