Newton's Laws for a Particle – A Level Mathematics B (MEI) OCR Revision

Newton’s Laws for a Particle

Newton’s first law, also known as the law of inertia, states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external unbalanced force.
This law is a foundational principle, explaining why objects keep doing what they are doing until an external force changes their motion.

Newton’s second law says that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is often expressed mathematically as F=ma where F is the force, m is the mass of the object, and a is acceleration.
This law makes quantitative predictions about motion: for instance, it tells you how much an object’s speed will change under the influence of a particular force.

Newton’s third law states that for every action, there is an equal and opposite reaction.
In other words, any force exerted on a body will create a force of equal magnitude but in the opposite direction on the object which exerted the first force.

A particle, in this context, is a theoretical object that has mass but no size.
When a particle is in equilibrium, the forces it experiences will cancel each other out, resulting in no acceleration.
When several forces act on a particle simultaneously, the net force or the resultant force can be found by vector addition of the individual forces.
If the resultant force is not zero, the particle will accelerate in the direction of the resultant force according to F=ma.
Constant motion (either rest or constant speed in a straight line) will occur only when the resultant force on a particle is zero.
Working with a particle simplifies the application of Newton’s laws as we don’t have to consider real-life complications such as size, shape and distribution of mass.