Units of Acceleration, Mass and Force
Newton's Second Law, usually written in the form
F = ma,
serves as the fundamental basis for the corresponding SI units:
- Acceleration: the vector acceleration a
of the body is the rate of change (with time t)
of the vector velocity v of the body,
which is itself the rate of change (with time t)
of the vector position x of the body (relative to a fixed origin),
whose magnitude x is measured in meters
(abbreviated "m", not to be confused with the mass m).
Thus the magnitude of the velocity, v, is measured in
meters per second (abbreviated "m/s" or m s-1")
and the magnitude of the acceleration, a, is measured in
meters per second per second (abbreviated "m/s2" or "m s-2").
- Mass: mass is measured in kilograms (kg),
a completely arbitrary unit.
A dozen small chicken eggs have a combined mass of about 1 kg.
- Force: A dimensional examination of the Second Law
shows that the magnitude of a vector force is measured in
"kg m s-2", a rather tedious expression
that has been named the Newton ("N") in honor of Sir Isaac.