Physics Homework Help With Linear Momentum

Linear Momentum

The momentum of a single particle is a vector linear momentum image defined as the product of its mass and its velocity linear momentum image1. That is

linear momentum image2

Suppose that instead of a single particle we have a system of n particle with masses m1, m2 … etc, and their velocities v1 and v2 etc. respectively then the total momentum linear momentum image3 in a particular reference frame is,

linear momentum image4
linear momentum image5
linear momentum image6

The vector sum of all external forces is given as, linear momentum image7

linear momentum image8
linear momentum image9
linear momentum image10

Taking its components along x-direction and y-direction we can write

linear momentum image11
linear momentum image12

This is nothing but Newton's second laws of motion. Note that no internal force will be used in this expression and only external forces will be used.

Conservation of Linear Momentum

If the sum of the external force acting on a system is zero. Then,

linear momentum image13

or linear momentum image14 = constant.

So, when the resultant external force acting on the system is zero, the total vector momentum of the system remains constant. This is called the principle of the conservation of linear momentum. The momentum of the individual particles may change, but their sum remains constant if there is no net external force.

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