Kinetic energy

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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.

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.

${\displaystyle \mathbf {F} \cdot d\mathbf {x} ={\frac {d\mathbf {p} }{dt}}\cdot d\mathbf {x} ={\frac {d\mathbf {p} }{dt}}\cdot \mathbf {v} dt=\mathbf {v} \cdot {\frac {d\mathbf {p} }{dt}}dt=\mathbf {v} \cdot d\mathbf {p} }$

but Potential Energy is not as can be seen here

${\displaystyle \mathbf {F} \cdot d\mathbf {x} =-\nabla V\cdot d\mathbf {x} =-{\frac {\partial V}{\partial x_{i}}}\cdot dx_{i}=-dV}$

which clearly suggests that only conservative forces can have potential energy associated with them; see conservation of energy.

The translational kinetic energy of an object is:

${\displaystyle E_{\text{translational}}={\frac {1}{2}}mv^{2}}$

where

${\displaystyle m}$ is the mass (resistance to linear acceleration or deceleration);

${\displaystyle v}$ is the linear velocity.

The rotational kinetic energy of an object is:

${\displaystyle E_{\text{rotational}}={\frac {1}{2}}I\omega ^{2}}$

where

${\displaystyle I}$ 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);

${\displaystyle \omega \ }$ is the angular velocity.