# How do you differentiate between momentum and kinetic energy?

Dec 31, 2017

see below

#### Explanation:

Consider an object with mass $m$ and velocity $v$

Its momentum is the product of the mass and velocity

momentum$= m v$

units are $k g \text{ "ms^(-1)" or } N s$

it is a vector quantity and so direction has to be assigned to the quantity.

its kinetic energy is the energy it has by virtue of its motion, and is defined as the work required in order to bring it to rest.

the equation to calculate its linear or translational $K {E}_{\text{lin}} = \frac{1}{2} m {v}^{2}$

if it is rotating it has rotational Kinetic energy and has the equation

$K {E}_{r o t} = \frac{1}{2} I {\omega}^{2}$

$I = \text{the moment of inertia about eh axis of rotation}$

$\omega = \text{the angular velocity}$

if it is rotating and traveling in a straight line the total KE is the sum of both components

the units are Joules , and KE is a scalar quantity.