Newton’s second law

EstablishedPhysics

\htmlClass{sjt-F}{\vec{F}} = \htmlClass{sjt-m}{m}\,\htmlClass{sjt-a}{\vec{a}}

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\vec{F}

Net forceRosetta entry →

Meaning

The vector sum of all forces acting on the object, in newtons (kg·m/s²).

Its job in this equation

The cause. The arrow marks it as a vector: it has a direction.

Picture it

The sum of every push and pull, as arrows added tip-to-tail.

Read it, progressively

1. Gist

Push harder and things speed up faster; heavier things speed up less for the same push.

What it does not establish

Fails near light speed (special relativity), in strong gravity (general relativity) and at atomic scales (quantum mechanics). It also needs an inertial frame: in a rotating frame you must add "fictitious" forces. It says nothing about which forces exist; those come from separate laws such as gravity and electromagnetism.

Play with it

F = ma · push a cart

Applied force F4 NMass m2 kg

Friction (μ = 0.3)

net force4.0 N

a = F/m2.00 m/s²

v0.00 m/s

x0.00 m

t0.0 s

Newton’s second law, a = F_net/m: the same push gives a heavy cart less acceleration. With friction on, only the net force accelerates the cart; push below the friction threshold and nothing moves. This form assumes constant mass and speeds far below light (non-relativistic). Simulated, not measured.

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