It is known that principle of Conservation of momentum and principle of conservation of energy are two fundamental principles of physics.But in RP Feynman's Lectures of physics, in the chapter of conservation of momentum, it is said that conservation of energy and conservation of momentum are consequences of Newtons laws of dynamics.Is it correct?
[Physics] Are principle of Conservation of energy and principle of conservation of momentum consequences of Newton’s laws
conservation-lawsenergy-conservationmomentumnewtonian-mechanics
Related Solutions
Momentum, energy, angular momentum, and charge are conserved locally, globally, and universally. One must remember that conservation locally (within a defined system) does not mean constancy. Constancy occurs only when the system is closed/isolated from the rest of the universe.
Conservation means that these quantities cannot spontaneously change. Let's consider momentum: the momentum of a system at a later time must equal the momentum at an earlier time plus the sum of the impulses applied to a system. The impluses in this sum could be adding or removing momentum from the system, but never creating nor destroying momentum: $$\vec{p}_{later}=\vec{p}_{before}+\Sigma\vec{J}_{during}.$$
For an isolated collision, without outside influence, $\vec{J}_{during}=0$, and $\vec{p}_{later}=\vec{p}_{before}$.
For the energy: $E_{later}=E_{before}+W+Q+\mathrm{radiation}$
For angular momentum: $\vec{L}_{later}=\vec{L}_{before}+\Sigma\vec{\Gamma}_{outside}$ ($\Gamma$ is torque on system)
For charge: $ Q_{later}=Q_{before}+\int I\;\mathrm{d}t$
In the case of kinetic energy, it is not universally conserved. It can appear and disappear as energy is transformed to different manifestations:heat internal energy, gravitational, electromagnetic, nuclear, all of which are energy. The total energy is conserved in a system (not necessarily constant), with the transfer agent being work/radiation/heat. The elastic collision is defined to be one in which the kinetic energy of the system remains constant.
Note that if you define a single object as the system of interest, neither the momentum nor the kinetic energy will remain constant during a collision with another object or while it falls in a gravitational field, but the momentum will be conserved (the object is subjected to impluses) and the energy of the object is conserved (outside forces do work).
Bottom line: Define a system, look for transfers of momentum (impulse), energy (work, etc), angular momentum (torque), and charge (current) into or out of the system. Then see if any of those conserved properties are also constant for your situation.
EDIT - Response to OP specific questions:
My specific question (in addition to the above) is: If in a collision there is a coefficient of restitution BELOW 1, doesn't that mean that the collision is INELASTIC? YES OR NO!
Yes. One may also call it partially elastic. If the coefficient of restitution is zero (0), the collision is completely inelastic.
And if that means that the collision IS INELASTIC, is it correct to use AT THE SAME TIME momentum conservation equation? YES OR NO!
Yes. Momentum is conserved in all collisions and explosions. And sometimes it might even be constant for short periods of time.
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.
Best Answer
Using Newton's Laws as a starting point, they are a consequence. Actually, Newton spoke in terms of momentum. Newton's 2nd Law actually says that force is equal to the change in momentum over time (which reduces to $F=ma$ if mass is constant). Newton's 3rd Law basically gives us conservation of momentum. If two objects impart equal and opposite forces on one another, for the same amount of time, then their change in momentum will also be equal and opposite.
Energy also traces back to Newton's Laws. A combination of the definition of work ($W = F \cdot \Delta x$), the Work-Energy theorem ($W _{net} = \Delta KE$), total energy ($E = KE + PE$), and ($F = -\Delta PE/\Delta x$) will show the conservation of energy. Alternatively, if you accelerate a mass with gravity and compare the kinetic and gravitational potential energy, or a spring-mass system and compare the kinetic and elastic potential energy, you will see that they are indeed conserved.
On the other hand, the 1st Law of Thermodynamics gives us the conservation of energy independent of Newton. Furthermore, both energy and momentum are conserved in quantum mechanics, where $F=ma$ is meaningless. With that in mind, we might say that Newton's Laws (stated as regarding forces) may be a consequence of our conservation laws, not the other way around.