Physics equations/04-Dynamics: Force and Newton's Laws/A:practice

Simple statement of Newton's third law
This popular statement of Newton's third law is somewhat misleading because the word "force" should be substituted for "action":

For every "action" there is and equal and opposite "reaction".

Also, this statement fails to emphasize that the two forces ALWAYS act on different objects. When making a free-body diagram with two or more objects, each object gets its own free body diagram.

Advanced statement of Newton's third law
The forces on a collection of N interacting particles can be described as either internal or external forces. Since forces are generally viewed as interactions between particles, the external force on the j-th particle, $$\vec F_j^\text{ext}$$ is an interaction with particles outside this collection of N particles. The sum of all forces on the jth particle is:


 * $$ m_j \vec a_j=\sum_{j=1}^N\vec F_{ji} + \vec F_j^\text{ext}$$

Newton's third law states that the internal force on the jth particle by the ith particle is $$\vec F_{ji}$$, and Newton's third law states that $$\vec F_{ji}=-\vec F_{ij}$$. Since the only number that equals its additive inverse is zero, it follows that no particle can exert a force on itself, e.g. $$\vec F_{ii} = 0$$ (for all i), and one wonders if the motion of physical objects could ever have been fathomed if particles could induce forces on themselves. When many particles are connected (either rigidly or by forces that allow relative motion), it can be shown that Newton's second law (F-ma) applies to the center-of-mass, defined as:

$$ \vec{R} = \frac{\sum_i m_i \vec{r}_i}{\sum_i m_i} = \frac{1}{M} \sum_i m_i \vec{r}_i $$ Physics equations