Newton's first law: things are lazy
Left alone, nothing changes its motion by itself. A ball on a flat table will not suddenly roll off, and a puck sliding on frictionless ice would keep gliding for ever. Objects only speed up, slow down or turn when something pushes or pulls them.
- Newton's first law
- An object stays at rest, or keeps moving at a constant velocity in a straight line, unless a resultant force acts on it. This reluctance to change motion is called inertia, and more mass means more inertia.
The key word is resultant. Forces almost always come in a crowd: gravity pulls a book down while the table pushes it up. When these cancel, the resultant is zero and the motion does not change. A car cruising at a steady 30 m/s has balanced forces just as truly as a parked car does.
Where this is assessed
Forces and motion sit mostly in Criterion A (recalling laws and applying equations) and Criterion C (processing data from motion experiments). Designing a fair test of, say, air resistance pushes into Criterion B, and evaluating your method is Criterion D.
Newton's second law: force, mass and acceleration
Once the forces do not balance, the object accelerates. The bigger the resultant force, the bigger the acceleration; the heavier the object, the smaller the acceleration for the same force. Newton tied these together in one tidy equation.
Here \( F \) is the resultant force in newtons (N), \( m \) is the mass in kilograms (kg), and \( a \) is the acceleration in metres per second squared (m/s\(^2\)). One newton is exactly the force needed to accelerate 1 kg at 1 m/s\(^2\).
A car of mass 1200 kg speeds up with an acceleration of 2.5 m/s\(^2\). What resultant force does the engine provide?
Check your units first
\( F = ma \) only gives newtons if mass is in kilograms and acceleration in m/s\(^2\). If a question gives grams or km/h, convert before you substitute, not after.
Newton's third law: forces come in pairs
You cannot push on something without it pushing back on you. When you jump, your feet push down on the ground and the ground pushes up on you with an equal force, and that upward push is what launches you.
- Newton's third law
- If object A exerts a force on object B, then B exerts an equal and opposite force on A. The two forces are the same size, point in opposite directions, and act on different objects.
That last detail matters. The action and reaction forces never cancel each other out, because they act on two different bodies. A rocket works this way: it throws hot gas backwards, and the gas pushes the rocket forwards.
Terminal velocity: when falling stops speeding up
Drop a skydiver and, at first, only weight acts, so they accelerate downwards. As they speed up, air resistance grows, because faster motion means hitting more air per second. Eventually the upward air resistance grows until it exactly balances the downward weight.
At that moment the resultant force is zero, so by Newton's first law the acceleration is zero. The skydiver keeps falling, but now at a steady speed called the terminal velocity.
| Stage of fall | Weight vs air resistance | Motion |
|---|---|---|
| Just released | Weight much greater | Accelerating fast |
| Speeding up | Air resistance rising | Accelerating, but less |
| Terminal velocity | Forces balanced | Constant speed |
Opening a parachute suddenly increases air resistance, so the forces are no longer balanced: the diver decelerates, then settles to a new, much lower terminal velocity that is safe for landing.
Momentum and its conservation
Momentum measures how hard something is to stop: a fast lorry and a slow bullet can both be dangerous for different reasons. It depends on both mass and velocity.
Momentum \( p \) is measured in kilogram metres per second (kg m/s). It is a vector, so direction counts: momentum to the right is positive, to the left is negative.
- Conservation of momentum
- In a collision or explosion with no external resultant force, the total momentum before equals the total momentum after. Momentum is neither created nor destroyed, only shared between the objects.
A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley and they stick together. How fast does the combined pair move afterwards?
Mind the direction
If two objects move towards each other, one momentum is positive and the other negative. Forgetting the minus sign is the most common momentum slip, and it usually gives an answer that is far too large.
Check yourself
Try each one on paper before opening the answer.
1. A resultant force of 12 N acts on a 3 kg box. What is its acceleration? +
Rearrange \( F = ma \) to \( a = \dfrac{F}{m} = \dfrac{12}{3} \). So \( a = 4 \) m/s\(^2\).
2. Explain, using forces, why a skydiver reaches a terminal velocity. +
As the diver falls faster, air resistance increases. It keeps rising until it is equal and opposite to the weight. The resultant force is then zero, so there is no acceleration and the diver falls at a constant terminal velocity.
3. A 0.5 kg ball travels at 4 m/s. What is its momentum, and what happens to the total momentum if it hits a wall and bounces back? +
Momentum \( = mv = 0.5 \times 4 = \) 2 kg m/s. When it bounces, momentum is still conserved for the ball-and-Earth system as a whole; the wall (and Earth) gains the momentum the ball loses, so the total stays the same even though the ball's own momentum reverses direction.
Part of the Physics library. Spotted an error or want a topic added? That feedback makes the notes better.