4 Newton’s Third Law
Newton’s third law describes the interactions of forces between multiple bodies. It states that the forces of two bodies on each other are always equal and in opposite directions. Mathematically, the third law can be written as
(7) F12 = − F21
where F12 is the force acting on body 1 due to body 2 and F21 is the force acting on body 2 due to body 1. There is also a rotational version of the third law:
(8) M12 = − M21
where M12 is the moment acting on body 1 due to body 2 and M21 is the moment acting on body 2 due to body 1. Newton’s third law is primarily used in developing equations of motion when there are multiple bodies interacting with each other, because it shows how the forces and moments (and therefore the position, velocity, and acceleration) of one body affect another.
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