A-level Mathematics/OCR/M1/Newton's Laws of Motion

Newton's first law of motion states that a body acted on by a balanced set of forces will stay at rest if it is at rest, and it will continue at a constant velocity if it is in motion. A common phrasing of the law is if the body is acted on by external forces however this is incorrect, for example a car can be acted on by no external forces and it can accelerate. This law is sometimes referred to as the law of inertia.

Newton's second law of motion states that if a body is acted on by an unbalanced set of forces then the resultant force equals the mass of the object times the acceleration of the object:

$$F = ma$$

Newton's third law of motion states that, in equilibria, every force has an equal and opposite reaction force.

These laws can be used (by themselves or in conjunction with other methods) to solve problems in M1. If a particle of mass m has a force acting on it of F, then its acceleration would be a. A numerical example of this would be a particle of mass 3 kg, being accelerated at a rate of 2 m/s^2 would require a force of 6N (kgm/s^2).

From Newton's second law of motion we gain the definition of the unit of force: the Newton, as the force required to accelerate a particle of mass one kg at a rate of 1 m/s^2. It has the units N, or in SI base units kg*m/s^2.