# Kinetic energy

**Kinetic energy** is the energy that an object has because of its motion. This energy can be converted into other kinds, such as gravitational or electric potential energy, which is the energy that an object has because of its position in a gravitational or electric field.

## Difference between Kinetic & Potential Energy

Kinetic Energy is the maximum amount of work a moving body due to its motion can do, whereas Potential energy is the maximum amount of work a body can do due to its configuration or position in a field force. Kinetic Energy is valid for all sorts of forces as seen from this derivation.

- <math> \mathbf{F} \cdot d \mathbf{x} = \frac{d \mathbf{p}}{dt} \cdot d \mathbf{x} = \frac{d \mathbf{p}}{dt} \cdot \mathbf{v}dt = \mathbf{v} \cdot \frac{d \mathbf{p}}{dt} dt = \mathbf{v} \cdot d \mathbf{p} </math>

but Potential Energy is not as can be seen here

- <math> \mathbf{F} \cdot d \mathbf{x} = - \nabla V \cdot d \mathbf{x} = -\frac{\partial V}{\partial x_i} \cdot dx_i = - dV </math>

which clearly suggests that only conservative forces can have potential energy associated with them.

## Translational kinetic energy

The **translational kinetic energy** of an object is:

- <math>E_{translational} = \frac{1}{2} mv^2 </math>

where

- <math> m </math> is the mass (resistance to linear acceleration or deceleration);
- <math> v </math> is the linear velocity.

## Rotational kinetic energy

The **rotational kinetic energy** of an object is:

- <math>E_{rotational} = \frac{1}{2} I \omega^2 </math>

where

- <math> I </math> is the moment of inertia (resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance from the axis of rotation);
- <math> \omega \ </math> is the angular velocity.