Linear momentum is a fundamental concept in physics that describes the motion of an object. It is defined as the product of an object's mass and its velocity. Mathematically, linear momentum (p) can be calculated using the equation: p = m * v, where m represents the mass of the object and v represents its velocity.

The conservation of linear momentum is a principle stating that the total linear momentum of an isolated system remains constant. This means that in the absence of external forces, the total momentum before an event is equal to the total momentum after the event.

For example, consider the following scenario: two objects of equal mass, initially at rest, are placed on a frictionless surface. If one of the objects starts moving to the right with a certain velocity, the other object will move to the left with the same velocity, demonstrating the conservation of momentum. The combined momentum of the two objects before and after the event is always zero, indicating conservation.

In another scenario, if an object of large mass collides with an object of small mass, the larger mass object will experience a smaller change in velocity compared to the smaller mass object, as momentum is conserved. This principle enables us to predict the post-collision velocities and directions of objects involved in collisions, making it a valuable tool in understanding various physical phenomena.