## Impulse-Momentum Principle

**Introduction: **Impulse is defined as the integral of force acting on an object, with respect to time. This means that impulse contains the product of force and time. Impulse changes the momentum of an object. As a result, a large force applied for a short period of time can produce the same momentum change as a small force applied for a long period of time. An impulse can act on an object to change either its linear momentum, angular momentum, or both.

In many real life problems involving impulse and momentum, the impulse acting on a body consists of a large force acting for a very short period of time — for example, a hammer strike, or a collision between two bodies.

**Concept of Impulse and Momentum:** **Work & Energy: **

- The concept of work relates force to displacement.
- More work done changes the motion of a system to a greater degree.
- That which is changed is called kinetic energy
- Scalar equation.

**Impulse & Momentum:**

- The concept of impulse relates force to time.
- Greater force or greater time of action is associated with more impulse applied.
- More impulse changes the motion of a system to a greater degree.
- That which is changed is called momentum.
- Vector equation.

**Consider Newton’s 2 ^{nd} law: **

mv (vector quantity) is called the linear momentum of the particle

**Linear impulse:**

**Rectangular coordinate system:**

The final momentum of a particle is obtained by adding vectorially its initial momentum and the impulse of the force F acting during the interval considered.