Dimensions

The dimensions of a physical quantity are the units reduced to mass, length and time; M, L and T.

1 Angles in degrees or radians have no dimensions. Ratios have no dimensions. (eg. mechanical advantage, coefficient of restitution etc.)

2 The terms of equations have the same dimensions.

In the equation ... mgh = 1/2 mu2 + 1/2 mv2

... the dimensions of each term are M L2 T-2.

3 Dimensional analysis can sometimes identify the possible powers in a power law. For instance, the period of oscillation of a water drop will depend on the surface tension, the density, and the radius.

If the period relationship is a power law, then ...

[T] = [s]a [r]b [r]c

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