Physics: Units and Measurement

Standards of Length, Mass, and Time

• Since 1983, the standard meter has been defined in terms of the distance light travels in a certain fraction of a second.
• Since 1967, the standard definition for the second has been based on the characteristic frequency of the cesium-133 atom.
• In mechanics, the three basic quantities used to derive additional quantities are mass, length, and time.
• The prefixes p, n, and G represent 10^-12, 10^-9, and 10^9 respectively.
• The ratio M/m of the prefixes M and m has a value of 10^9.

The Building Blocks of Matter

• The nuclei of atoms contain protons and neutrons.
• The existence of the neutron was confirmed in 1932.
• The proton contains two up quarks and one down quark.

Dimensional Analysis

• Velocity can be expressed as at, where a is acceleration and t is time.
• The expression v/x is dimensionally consistent with an expression that would yield a value for time^-1.
• If the displacement of an object, x, is related to velocity, v, according to the relation x = Av, the constant A has the dimension of time.
• The speed of a boat in 5 knots can be expressed in the SI system of units as m/s.
• The equation t = x/v is dimensionally correct, but v = a/t is not.
• If an equation relating position, x, to time, t, is given by x = bt^3 + ct^4, the dimensions of b and c are L/T^3 and L/T^4 respectively.