Newton's Second Law

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We have seen Newton's Second Law expressed as:

but actually, Newton didn't express it in that form. This statement is only valid if the mass of the object (or objects) in question is constant. Granted, this is often the case - but not always. As a rocket fires its engines, it loses mass as fuel is ejected, for instance. What Newton actually said was much more powerful and general - something like:

The net force on an object (or system of objects) equals the rate at which the object's momentum changes.

Symbolically, this can be expressed as:

where "p" is used as the mathematical symbol for momentum. It can be shown that this is the same as:

Fnet = ma + v(rate the mass changes)

If the mass of an object doesn't change, the rate its mass changes is zero, so the second term in this equation disappears. You are left with the "good old" F = ma Newton's Second Law. In the case of a rocket or other system whose mass changes, the more complicated form of Newton's Second Law must be used instead. The point is that Newton's Second Law was actually expressed in terms of the change in momentum of a system - not its acceleration.

last update April 10, 2000 by JL Stanbrough