Conservation laws of momentum and energy are said to be the most basic principles of physics. Are they also valid for non-inertial frames, and in what way?

  • $\begingroup$ Newton's laws are only valid in inertial systems. In non-inertial systems all bets are off. $\endgroup$ – CuriousOne Jun 11 '16 at 20:42
  • $\begingroup$ Welcome to Physics SE Nabin. Please note the site policy : questioners are expected to show some effort to answer the question themselves. What do you think and why? Have you tried to find an answer on the internet? $\endgroup$ – sammy gerbil Jun 11 '16 at 21:10
  • $\begingroup$ How many examples (say of balls bouncing off other balls) did you work through before you posted this question? $\endgroup$ – WillO Jun 11 '16 at 21:31

Regarding total momentum conservation, the point is that in non-inertial reference frames inertial forces are present acting on every physical object. Momentum conservation is valid in the absence of external forces.

However, if these forces are directed along a fixed axis, say $e_x$, or are always linear combinations of a pair of orthogonal unit vectors, say $e_x,e_y$, (think of a frame of axes rotating with respect to an inertial frame around the fixed axis $e_z$ with a constant angular velocity), conservation of momentum still holds in the orthogonal direction, respectively. So, for instance, in a non-inertial rotating frame about $e_z$, conservation of momentum still holds referring to the $z$ component.

Mechanical energy conservation is a more delicate issue. A general statement is that, for a system of points interacting by means of internal conservative forces, a notion of conserved total mechanical energy can be given even in non-inertial reference frames provided a technical condition I go to illustrate is satisfied.

Let us indicate by $I$ an inertial reference frame and by $I'$ the used non-inertial frame. Assume that our physical system is made of a number of points interacting by means of conservative true forces depending on the differences of position vectors of the points, so that a potential energy is defined and it does not depend on the reference frame.

If the origin of $I'$ has constant acceleration with respect to $I$ and the same happens for the angular velocity $\omega$ of $I'$ referred to $I$ (it is constant in magnitude and direction), then only three types of inertial forces take place in $I'$ and all them are conservative but one which does not produce work (Coriolis' force). In this case, the sum of the kinetic energy in $I'$, the potential energy of the true forces acting among the points and the potential energy of the inertial forces appearing in $I'$ turns out to be conserved in time along the evolution of the physical system.


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