Newton's Laws of Motion – A Level Mathematics B (MEI) OCR Revision

Newton’s Laws of Motion

Mechanics is all about understanding and predicting how objects move. The main forces to understand are gravity, friction, and tension.
Gravity is the force that attracts two objects towards each other. It is always acting downwards and is proportional to the object’s mass.
Friction is the force that opposes the motion of an object. This can exist between solid surfaces, layers of fluid, or even within an object itself.
Tension is the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.

The understanding of how objects move is framed in the context of Newton’s laws of motion.
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.
Newton’s second law avers that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it’s expressed as F=ma; where F is the force, m is the mass of the object, and a is acceleration.
Newton’s third law establishes that for every action, there is an equal and opposite reaction. Essentially, any force that is exerted on a body will create a force of equal magnitude but in the opposite direction on the object that exerted the first force.

The forces on a particle, a theoretical object possessing mass but having negligible size, can offer more insights when Newton’s laws are applied.
In an equilibrium state, the forces a particle experiences will cancel out each other, giving rise to zero acceleration.
When a particle has multiple forces acting upon it at once, the resultant force or the net force can be worked out by way of vector addition of the individual forces.
A particle will accelerate in the direction of the resultant force when the resultant force is not zero, according to F=ma.
A state of constant motion (either resting or moving at constant speed in a straight line) will persist only when the resultant force acting on a particle is zero.
Utilising a particle in the clarification of Newton’s laws eliminates real-life complications like accounting for size, shape and distribution of mass and simplifies the application of said laws.