How Does the Principle of Relativity Ensure Particle L Stays on the 3-Axis?

[cleggy]

1.

I'm asked to apply the principle of relativity in Newtonian physics to show that particle L cannot leave the 3-axis and to explain why the identical nature of particles J and K is crucial.

2.

An isolated system consists of 3 particles J, K and L

J and K have mass m and are identical. L has mass M.

In an inertial frame P the initial positions and velocities are :

For J : x(0)= (-3,4,0) v(0)= (0,2,-1)

For K : x(0)= (3,-4,0) v(0)= (0,-2,-1)

For L : x(0)= (0,0,4) v(0)= (0,0,2)

In an inertial frame P' the initial positions and velocities are :

For J : x(0)= (3,-4,0) v(0)= (0,-2,-1)

For K : x(0)= (-3,4,0) v(0)= (0,2,-1)

For L : x(0)= (0,0,4) v(0)= (0,0,2)


3. The Attempt at a Solution

I'm not sure where to start. Does it hace anything to do with if L leaves the 3-axis then P and P' will be able to tell their reference frames apart from one another?

 

[NateD]

The principle of relativity states that all inertial frames are equivalent, meaning that the laws of physics are the same regardless of which frame you are in. As such, it follows that particle L cannot leave the 3-axis, as this would mean that one frame is different from the other. The identical nature of particles J and K is crucial because it ensures that both frames are equivalent. If they were not identical, then the two frames would be different, and particle L could leave the 3-axis. This is because the initial positions and velocities of the particles will be different in each frame, resulting in different trajectories for each particle in each frame.