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In the formula F=ma, F N stands for the resultant force acting on a particle, m kg is the mass of the particle and a m/sē is the acceleration produced.
Remember that mass is a scalar quantity, a measure of the amount of matter in an object. Whereas weight is a vector quantity, the force that acts upon objects subject to gravity. On the earth, the force of weight is always directed towards the centre of the earth.

## Summary/Background

Sir Isaac Newton (4 January 1643 - 31 March 1727) was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.
Newton's laws of motion are three physical laws which provide relationships between the forces acting on a body and the motion of the body, first compiled by Sir Isaac Newton. Newton's laws were first published together in his work Philosophiae Naturalis Principia Mathematica (1687). The Principia is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another.

The laws form the basis for classical mechanics.
1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
2. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
3. For every action there is an equal and opposite reaction.

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## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)M1DynamicsNewton's Laws-
AQA AS Maths 2017MechanicsForces and Newton's LawsNewton's Laws-
AQA AS/A2 Maths 2017MechanicsForces and Newton's LawsNewton's Laws-
CCEA A-Level (NI)M1DynamicsNewton's Laws-
CIE A-Level (UK)M1DynamicsNewton's Laws-
Edexcel A-Level (UK - Pre-2017)M1DynamicsNewton's Laws-
Edexcel AS Maths 2017MechanicsForces and Newton's LawsNewton's Laws-
Edexcel AS/A2 Maths 2017MechanicsForces and Newton's LawsNewton's Laws-
OCR A-Level (UK - Pre-2017)M1DynamicsNewton's Laws-
OCR AS Maths 2017MechanicsForces and Newton's LawsNewton's Laws-
OCR MEI AS Maths 2017MechanicsForces and Newton's LawsNewton's Laws-
OCR-MEI A-Level (UK - Pre-2017)M1DynamicsNewton's Laws-
Pre-U A-Level (UK)MechDynamicsNewton's Laws-
Universal (all site questions)DDynamicsNewton's Laws-
WJEC A-Level (Wales)M1DynamicsNewton's Laws-