# Linear Momentum

### Definition of Linear Momentum

• Linear momentum (p) is a vector quantity that denotes the product of an object’s mass (m) and its velocity (v).

• It is represented by the letter ‘p’ and its unit is kilogram meter per second (kg m/s) in the SI system.

• Mathematically, it’s defined as p = mv where ‘m’ is the mass of the object and ‘v’ is the velocity.

### Conservation of Linear Momentum

• The principle of conservation of momentum states that the total momentum of an isolated system of objects remains constant, provided no external forces act upon it.

• Whenever objects interact, their total linear momentum before the interaction is equal to their total linear momentum after the interaction.

• This principle is useful in a variety of physics problems, including collisions and explosions.

### Impulse and Linear Momentum

• Impulse (J) is the change in an object’s momentum, caused by the application of a force over an interval of time.

• Mathematically, Impulse is defined as J = Δp = Ft, where ‘Δp’ represents the change in momentum, ‘F’ denotes the force applied and ‘t’ is the time for which the force is applied.

• This relation is often referred to as the impulse-momentum theorem.

### Applications of Linear Momentum

• Linear momentum is used in various aspects of physics and engineering, including calculating effects of forces, and solving problems related to collisions.

• Understanding momentum plays a vital role in road safety, as many crash-protection features in cars are designed based on the principles of momentum conservation.

### Understanding Linear Momentum

• Familiarise yourself with the concept of linear momentum, its mathematical representation and units of measurement.

• Understand and apply the principle of conservation of momentum to solve problems involving interaction of objects.

• Learn the relationship between momentum, force, and time, often referred to as impulse.

• Be capable of applying these concepts to various practical situations, from engineering designs to road safety.

Linear momentum is a fundamental concept in physics that describes the motion of objects. It is particularly useful when analysing collisions and interactions between objects, and forms an essential part of a physicist’s toolkit.