Work

In physics, work refers to the dot product of force and distance vectors .

<math>W = \vec{F} \cdot \vec{d}</math>

Or:

<math>W = Fd \cos{\theta}</math>

Where θ is the angle that separates the vectors. The second form of the equation is the expanded form of the "dot product" in the first equation. In physics, the dot product <math>\vec{a} \cdot \vec{b}</math> (read "a dot b") can be rewritten as <math>|\vec{a}| |\vec{b}| \cos{\theta}</math>.

When the force is not constant, the correct expression uses integration:

<math>\int \vec{F} \cdot \mathrm{d}\vec{s}</math>

Work is a transfer of energy; if <math>W</math> is positive, there is a transfer of energy to the system, and if <math>W</math> is negative there is a transfer of energy from the system.

Its units are that of force multiplied by distance, in SI this is Newton · Meter, or Joule. The aberrant unit kWh (kilowatt-hour) is sometimes used; this unit is the product of kilowatt, or 1,000 Watts (Joules per second), and hour, or 3,600 seconds.