Kinematics described motion; dynamics explains it. Newton's laws tie force to the way motion changes, and the deepest single statement is that a force is the rate of change of momentum. Get that, and F = ma falls out as a special case.
Mass measures inertia, the resistance to a change in motion. Newton's first law: with no resultant force, velocity stays constant. Second law: the resultant force equals the rate of change of momentum, F = Δp / Δt, which for constant mass becomes F = ma. Third law: forces come in pairs that are equal, opposite, of the same type, and act on two different bodies. Weight is the pull of gravity, W = mg.
A constant force pushes a cart on a frictionless track. The acceleration follows a = F / m, so it rises with force and falls with mass. Change both, watch the cart respond, then predict what doubling the mass does to the acceleration.
| Law | Statement | In symbols |
|---|---|---|
| First | An object stays at rest or moves at constant velocity unless acted on by a resultant force | F = 0 ⇒ a = 0 |
| Second | The resultant force equals the rate of change of momentum | F = Δp / Δt = ma |
| Third | If A exerts a force on B, then B exerts an equal and opposite force of the same type on A | Fₕ₋ = −F₋ₕ |
Linear momentum is p = mv, a vector pointing along the velocity, measured in kg m s⁻¹. The second law in full, F = Δp / Δt, also handles cases where mass changes, but at AS you most often use the constant-mass form F = ma.
Four quick checks on the laws, F = ma and momentum. Each correct answer earns XP and lights this skill on your star map.
In the simulator, keeping the force fixed and increasing the mass causes the acceleration to:
The property of an object that measures its resistance to a change in motion is its:
A 1500 kg car travels at 20 m s⁻¹. Its linear momentum is:
Newton's second law in its most general form states that the resultant force is equal to the:
The classic error is to pair the weight of an object with the normal contact force from the surface it rests on. They act on the same body and can be different types and sizes (think of an object on a slope), so they are not a third-law pair. A true pair always acts on two different bodies and is the same type of force. Also keep mass and weight distinct: mass (kg) is the same everywhere, while weight (N) is mg and changes with g.
Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A resultant force of 12 N acts on a 3.0 kg trolley. Its acceleration is:
A 0.16 kg ball hits a wall at 8.0 m s⁻¹ and rebounds at 6.0 m s⁻¹ in the opposite direction, in a contact time of 0.040 s. The average force on the ball is:
A book rests on a table. Which force is the Newton's third law pair of the gravitational pull of the Earth on the book?
A 2.0 kg object is pulled along a rough surface by a 10 N force while a 4.0 N friction force opposes it. Its acceleration is:
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