Definition · Plain-language
Newton’s second law
Newton’s second law states that the acceleration of an object is proportional to the net force on it and inversely proportional to its mass, captured by F = ma.
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What F = ma means
Newton’s second law turns the first law into a precise equation: the net force F acting on an object equals its mass m times its acceleration a, so F = ma. Acceleration means any change in velocity — speeding up, slowing down or changing direction. The equation says two things at once. First, for a fixed mass, doubling the force doubles the acceleration. Second, for a fixed force, doubling the mass halves the acceleration. This is why a powerful engine in a light car gives brisk acceleration, while the same engine in a heavy lorry produces far less.
Force, mass and acceleration are vectors
Force and acceleration are vector quantities — they have both size and direction — and the second law says the acceleration is always in the same direction as the net force. Force is measured in newtons (N): one newton is the force that gives a one-kilogram mass an acceleration of one metre per second squared. Rearranging F = ma lets you solve for any unknown: a = F ÷ m gives acceleration from force and mass, and m = F ÷ a gives mass. This single relationship underlies the calculation of everything from rocket thrust to the grip a tyre needs in a corner.
The deeper form: rate of change of momentum
Newton actually stated the law in terms of momentum — the product of mass and velocity. In its general form, the net force equals the rate at which an object’s momentum changes over time. When mass is constant, this reduces to the familiar F = ma. The momentum form is more powerful because it also handles systems whose mass changes, such as a rocket burning and ejecting fuel, where the loss of mass is part of how the force arises. For most everyday problems, however, F = ma is the practical tool.
Key facts
At a glance
- Definition: net force equals mass times acceleration
- Equation: F = ma
- Deeper form: force equals the rate of change of momentum
- Direction: acceleration points the same way as the net force
- Units: force in newtons (N); 1 N accelerates 1 kg at 1 m/s²
- Rearranged: a = F ÷ m, so heavier objects accelerate less for the same force
Common misconceptions
What people often get wrong
Often heard: A constant force makes an object move at a constant speed.
Actually: A constant net force produces a constant acceleration, so the object keeps speeding up. Constant velocity requires zero net force, as the first law states.
Often heard: In F = ma, the F is just any force acting on the object.
Actually: F is the net force — the vector sum of all forces. If several forces act, you must add them first; only the leftover, unbalanced force produces acceleration.
Often heard: Mass and weight are the same thing in the equation.
Actually: Mass is the amount of matter and resists acceleration; weight is the force of gravity on that mass (weight = mass × gravitational field strength). The m in F = ma is mass, not weight.
Going deeper
