Units

Quantities

A scalar quantity has a magnitude, but no direction. A scalar is written as a plain letter, like s.

A vector quantity has both a magnitude and a direction (in any number of dimensions). A vector is written as a letter with an arrow above, like \vec{v}.

Units

Force

Force (F) is measured in newtons (N), equivalent to \kg\m\s^{-2}.

\vec{F} = m\vec{a}

Weight force is force due to mass and gravity:

\vec{F_w} = mg

Energy

Energy (E) is measured in joules (J), equivalent to newton-meters or \kg\m^2\s^{-2}. It is force over distance.

Kinetic energy (E_k) is energy possessed from speed (not velocity), or the energy required to attain that speed. It is given by:

E_k = \frac{1}{2}mv^2

Gravitational potential energy (E_p) is energy possessed from height, or the energy required to attain that height (oppose gravity over a distance). It is given by:

E_p = mgh

Work

Work (W) is done when energy is transformed from one form to another (expended), and is measured in joules (same as energy).

The work done when using a force F to move an object by a distance d is given by:

W = Fd

For a force that varies over time, the work done is given by the total area beneath a graph of force vs distance, which can be calculated via definite integration.

Power

Power (P) is measured in watts (W). It is the rate of change of work, measuring the rate in which work is done, and is given by:

P = \frac{\Delta W}{\Delta t}