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/s² 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.

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.

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.

- Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
- 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.
- For every action there is an equal and opposite reaction.

## Software/Applets used on this page

## Glossary

### acceleration

the rate of change of velocity with time. It is a vector quantity with magnitude and direction.

### body

an object with both mass and size that cannot be taken to be a particle

### calculus

the study of change; a major branch of mathematics that includes the study of limits, derivatives, rates of change, gradient, integrals, area, summation, and infinite series. Historically, it has been referred to as "the calculus of infinitesimals", or "infinitesimal calculus".

There are widespread applications in science, economics, and engineering.

There are widespread applications in science, economics, and engineering.

### centripetal

of a force directed towards the centre in circular motion

### force

that which causes a body to accelerate or change in momentum

### gravity

the force that the Earth exerts on all objects. It acts towards the centre of the Earth.

If the mass of the object is m kg then this force is defined to be mg Newtons, where g is the acceleration due to gravity.

If the mass of the object is m kg then this force is defined to be mg Newtons, where g is the acceleration due to gravity.

### integral

the anti-derivative

### mass

a measure of the quantity of matter in an object

### newton

the unit of force

### particle

an object with negligible size and internal structure, which can be represented by a point; the fundamental assumption in mechanics.

### scalar

A mathematical object with one property of magnitude or size.

### union

The union of two sets A and B is the set containing all the elements of A and B.

### vector

A mathematical object with magnitude and direction.

### weight

a force which acts upon masses in a gravitational field. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass. Weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a force that results from the action of gravity on matter: it measures how strongly gravity pulls on that matter.

### work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AQA A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws |

AQA AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws |

AQA AS/A2 Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws |

CCEA A-Level (NI) | M1 | Dynamics | Newton's Laws |

CIE A-Level (UK) | M1 | Dynamics | Newton's Laws |

R Mechanics - Forces and Newton | R1 Newton First Law | Newton's Laws | |

Edexcel A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws |

Edexcel AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws |

Edexcel AS/A2 Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws |

OCR A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws |

OCR AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws |

OCR MEI AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws |

OCR-MEI A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws |

Pre-U A-Level (UK) | Mech | Dynamics | Newton's Laws |

Universal (all site questions) | D | Dynamics | Newton's Laws |

WJEC A-Level (Wales) | M1 | Dynamics | Newton's Laws |