Define and explain the impulse-momentum theorem.

The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it.

The impulse-momentum theorem is a fundamental principle in physics that connects the concepts of force and motion. It is derived from Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In the context of the impulse-momentum theorem, impulse is defined as the integral of a force, F, over the time interval, t, for which it acts. This means that impulse is the total effect of a force acting over time.

Momentum, on the other hand, is a vector quantity that is defined as the product of an object's mass and its velocity. It describes the motion of the object. The change in momentum, also known as delta p, is the difference between the final and initial momentum of the object.

The impulse-momentum theorem, therefore, states that the change in momentum of an object is equal to the impulse applied to it. Mathematically, this can be expressed as Ft = Δp, where F is the force applied, t is the time over which the force is applied, and Δp is the change in momentum.

This theorem is particularly useful in analysing collisions and impacts. For example, when a cricket ball is hit by a bat, the force of the bat over the contact time changes the ball's momentum, causing it to move in the opposite direction. Similarly, when a car hits a wall, the force of the impact over the time of contact changes the car's momentum to zero, causing it to stop.

In conclusion, the impulse-momentum theorem is a fundamental concept in physics that provides a relationship between force, time, and the change in momentum. It is a powerful tool for understanding and analysing the effects of forces on the motion of objects.