Theory of Everything - View Single Post

AntonioLao · 04-22-2005, 11:43 AM

Quote:

Originally Posted by GUILLE

One more thing, how is the momentum of an object calculated?

From classical mechanics -
In an idealized frictionless system, the momentum of a point object of mass m and velocity v is given by mv. If there are no other object in the system, the velocity remains constant. But when interaction with one other object occurs then the vector sum of momentum remains constant. This is the conservation law for linear momentum and is a direct demonstration of Newton's 3rd law of motion.

$m_1 v_1 + m_2 v_2 = 0$

and the time rate of change of linear momentum is the inertial force.

$F_1 = m_1 \frac{d v_1}{d t}$

$F_2 = m_2 \frac{d v_2}{d t}$

therefore

$F_1 + F_2 = 0$ or $F_1 = - F_2$

for every action there is an equal and opposite reaction.

But real objects are not point-particles, therefore in analytical mechanics, a center of mass is defined to account for linear momentum as well as angular momentum. Note that angular momentum is also conserved.

In relativistic mechanics, the time rate of change of mass is not zero, i.e., mass is not a constant.