# Work Energy Theorem

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According to this theorem, the work done by all the forces (conservative or non-conservative, external or internal) acting on a particle or an object is equal to the change in kinetic energy of it.

$\Rightarrow W_{net} = \Delta K.E. = K_f - K_i$

Let $\overrightarrow{F_1}$, $\overrightarrow{F_2}$ ... be the individual forces acting on a particle. The resultant force is $\overrightarrow{F} = \overrightarrow{F_1} + \overrightarrow{F_2} + ...$ and the work done by the resultant force is:

$W = \int{ \overrightarrow{F} \cdot \overrightarrow{dr} } = \int {( \overrightarrow{F_1} + \overrightarrow{F_2} + ... ) \cdot \overrightarrow{dr} }$
$= \int{ \overrightarrow{F_1} \cdot \overrightarrow{dr} } + \int{ \overrightarrow{F_2} \cdot \overrightarrow{dr} + ...}$

where $\int{ \overrightarrow{F} \cdot \overrightarrow{dr} }$ is the work done on the particle by $\overrightarrow{F_1}$ and so on. Thus, work energy theorem can also be written as: Work done by the resultant force is equal to the sum of the work done by the individual forces. There are a few points worth noting:

1. ) If Wnet is positive then Kf - Ki = +ve (positive), i.e, Kf > Ki or kinetic energy will increase and vice versa.
2. ) This theorem can be applied to non-inertial frames also. In a non-inertial fram it can be written as: Work done by all the forces (including pseudo forces) = change in kinetic energy in non-inertial frame.