# Doubt in law of mutual interaction

Book: Classical mechanics (textbook) by Douglas Gregory (cambridge publications)

Law of mutual interaction states that when two particle (let it be P1 and P2) interacts, the particle (P1) induces an instantaneous acceleration (a21) on particle P2 and the particle P2 induces an instantaneous acceleration (a12) on particle (P1).

If the (inertial)masses of the particles are same, then the magnitude of acceleration be the same, and the ratios of acceleration will be constant ( for this case it is 1)(consistency relation) That is what Newton's third law says.

My question is, for different (inertial)masses the ratio will be constant ( but not unity) ( it does not satisfy consistency relation) Am i right?

If yes My question is consistency relation is important in classical mechanics?

• Comment to the question (v3): Please clarify the notion of "consistency relation" used here. – Qmechanic Nov 1 '13 at 19:47

As far as I can tell, Newton's third law says "action = reaction" which refers to the mutual forces between the two particles, not to the acceleration directly. But from this it follows that the ratio of acceleration of the two particles must the constant without external forces acting on the particles because: $F_1 = m_1 \cdot a_1$ and $F_2 = m_2 \cdot a_2$. Due to action = reaction: $F_1 = -F_2$. Hence: $a_1/a_2 = -m_2/m_1$, which is constant if the particle masses are constant. (Equations are meant as one per spatial direction.)