# Conservation of Momentum, Rest and Motion

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## Mechanics

The branch of physics that deals with the various aspects of motion is called Mechanics. Mechanics comprises subtopics like kinematics,dynamics and statics. Kinematics is the study of the description of motion. Dynamics is the study of the cause of motion. Statics is the study of the state of rest or the equilibrium of a body.

## Rest and Motion

The concept of particle is very useful in the description of motion of a body. A particle is a point mass. That is, an object without any extent. A real object having a definite shape and size can be treated as a particle when its dimensions are very small compared to the distance travelled by it. For example, the moon orbiting the earth can be considered as a particle since the radius of the moon is very small compared to the radius of its orbit around the earth.The concept of rest and motion can be explained by considering an object as a particle.

If a particle occupies the same position at all instants of time with respect to its surroundings then it is said to be at rest. If the particle occupies different positions at different instants of time with respect to its surroundings then it is said to be in motion.

## Newton’s Laws of motion

In particle kinematics the motion of the particle is described by explaining terms like displacement, velocity and acceleration. However, the basic question “ What causes this motion?” was not dealt with. Dynamics is the branch of mechanics that answers to the above question in terms of force and inertia. The relation between the force acting on the body and the motion executed by the body is governed by Newton’s laws of motion.

### Newton’s first law of motion

The law states that “ Every body continues to be in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by an external force impressed on it”.

### Newton’s second law of motion

The law states that “The time rate of change of momentum is directly proportional to the impressed force and takes place in the direction of the force”. The linear momentum is measured by the product of mass and velocity of the body.

### Newton’s third law of motion

The third law states that “To every action there is an equal and opposite reaction”

## Law of Conservation of Momentum

Conservation of momentum is a consequence of Newton’s second law of motion and third law of motion. The law of conservation of momentum which can be detected from Newton’s second law and third law of motion is an important law in mechanics. The law is especially useful for solving problems which deal with the collisions between particles. The law states that “ The total momentum of an isolated system of interacting particles is conserved”.

## Examples of Conservation of Momentum

• When the bullet is fired from the gun, the bullet moves forward towards the target while the gun recoils (moves backward).
• When a body of mass M explodes into two parts of equal masses then the two parts will move with equal speeds in opposite directions.