Revise Momentum and Newton's laws of motion for Cambridge 9702 (3.1)

Momentum is a measure of an object's motion that considers both its mass and its velocity. It's a vector quantity, meaning it has both magnitude and direction. Think of it as how much 'oomph' an object has – a heavy, fast object has more momentum than a light, slow one.

$p = mv$

Sir Isaac Newton's laws are foundational to physics, explaining how forces affect motion. They govern everything from everyday pushes and pulls to the orbits of planets. Understanding them is crucial for mastering mechanics.

An object will remain at rest, or continue to move at a constant velocity, unless acted upon by a net external force. This law introduces the concept of inertia – an object's resistance to changes in its state of motion.

The net force acting on an object is directly proportional to its acceleration and inversely proportional to its mass. Crucially, the net force is also defined as the rate of change of the object's momentum. Force causes momentum to change.

$F_{net} = ma$ $F_{net} = \frac{\Delta p}{\Delta t}$

Impulse is a concept directly derived from Newton's Second Law. It is defined as the product of the average net force and the time interval over which it acts. Impulse is also equal to the change in momentum of the object. This relationship is particularly useful for analysing situations involving large forces acting over short times, like collisions or impacts.

$Impulse = F_{avg} \Delta t = \Delta p$

For every action force exerted by one object, there is an equal magnitude and opposite direction reaction force exerted by a second object. It's critical to remember these forces always act on different bodies, meaning they never cancel each other out on a single object.

Often confused, mass and weight are distinct concepts. Mass is a scalar quantity measuring the amount of matter in an object and its inertia. Weight is a vector quantity representing the gravitational force exerted on an object. Your mass is constant, but your weight changes with gravitational field strength.

$W = mg$

The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external resultant force acts on it. In simpler terms, the total momentum before an interaction, like a collision, will always equal the total momentum after.

Collisions are classified by whether kinetic energy is conserved during the interaction, while momentum is always conserved in a closed system.

When an object falls through a fluid (like air), it experiences resistive forces (e.g., air resistance or drag). As speed increases, these forces grow. Terminal velocity is reached when the downward driving forces (like weight) are perfectly balanced by the upward resistive forces, leading to zero net force and constant maximum speed.