Doubt in Law of mutual interaction

In summary, the law of mutual interaction in classical mechanics states that when two particles interact, they induce instantaneous accelerations on each other. If the masses of the particles are equal, the magnitude of the accelerations will be the same and the ratio of accelerations will be constant. This is known as the consistency relation. Newton's third law states that if P1 interacts with P2, then P2 will interact with P1 with an equal but opposite force, and the ratio of the accelerations will depend on the masses. There are no issues with consistency in this scenario and the ratio of accelerations will still be constant, but not unity, for different masses. Therefore, consistency is an important concept in classical mechanics.
  • #1
manimaran1605
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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?
 
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  • #2
If P1 interacts with P2 then Newton's 3rd law of motion implies that P2 interacts with P1 with an "equal but opposite " force. Then if the masses are M1 and M2 we will have M1*a1 = - M2*a2, and the ratio of the accelerations can be seen to depend upon the masses.

I don't see what your concern is.
 
  • #3
It is a core topic in classical mechanics sir.
 
  • #4
Let me restate: I don't understand what the question is - the algebra seems clear.

I don't see any problems with "consistency" - classical mechanics is self-consistent.
 
  • #5
manimaran1605 said:
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
The ratio of the accelerations will be constant but not unity for different masses (and it will be the ratio of the masses, themselves constant so it's not surprising that the ratio of the accelerations is constant). This does not violate any consistency condition.
 
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Related to Doubt in Law of mutual interaction

1. What is the Law of Mutual Interaction?

The Law of Mutual Interaction, also known as Newton's Third Law of Motion, states that for every action, there is an equal and opposite reaction.

2. How does the Law of Mutual Interaction apply to the field of law?

In the field of law, the Law of Mutual Interaction can be applied in cases where there are conflicting parties or interests. Just as in physics, where one force will always have an equal and opposite force acting upon it, in law, one party's actions will always have a reaction from the other party.

3. Can the Law of Mutual Interaction be used to resolve disputes in court?

Yes, the Law of Mutual Interaction can be used in court to resolve disputes. By understanding that every action has an equal and opposite reaction, judges and lawyers can consider the actions of both parties and determine a fair resolution.

4. How does the Law of Mutual Interaction relate to the concept of causation?

The Law of Mutual Interaction is closely related to the concept of causation. In both cases, there is an action that leads to a reaction. In law, causation is used to determine whether an action caused a certain outcome, while in physics, the Law of Mutual Interaction explains the relationship between two forces.

5. Are there any exceptions to the Law of Mutual Interaction?

While the Law of Mutual Interaction is a fundamental principle in physics, there are some exceptions that have been observed in certain scenarios, such as at the atomic level. However, in the field of law, the principle of mutual interaction remains a fundamental concept and is applicable in most situations.

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