What does it mean if a body has kinetic energy?
Does it mean that the momentum vectors of each particle of that body has the same direction?
What about angular momentum?
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3 Answers
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Imagine that you have just two particles with the same mass and same speed, but going in opposite directions. They have opposite momenta, so the total momentum is zero. But they each have energy, and the total energy is not zero. The reason is because kinetic energy is just $\frac{1}{2} m v^2$. That square means that the kinetic energy can never be negative, so it can never cancel out kinetic energy from something else. And the directions of the velocity vectors don't come into it -- just the "lengths".
Another good example is a gas. The gas molecules will be going all sorts of different directions, so their momenta will be in all sorts of different directions. But the total momentum can still be zero, while the total kinetic energy will be proportional to the temperature.
Energy, momentum, and angular momentum are completely separate things, that need to be measured separately. The only thing you can say is that if there is no kinetic energy, then there is no momentum and no angular momentum. But you could still have kinetic energy with no net momentum. You could also have momentum without angular momentum, or angular momentum without any net momentum.
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energy is always positive or 0. And these are just numbers we associate with a body due to its motion according to different set of mathematical rules so that we can study these particles . As such they have no physical meaning . For example momentum is just $m$ x $\vec v$ . It is just a number we associated with a body by the quantities we defined ourselves as mass and velocity in the first place and similarly for $\vec L$ and $K.E.$ according to different set of mathematical rules .
A body having Kinetic Energy in the classical sense means that it is moving or parts of it are moving . And for momentum and angular momentums, it is just numbers we defined so that we can study the forces and torques caused by interactions . You don't measure interactions , you measure their effect felt . And to measure that effect and to predict the future and past using those effects , you observe that there are certain mathematical quantities in whose terms the effects are felt . For example , the force is felt/defined/calculated as rate of change of $\vec p $ and all of these numbers are assigned by us to the body so that we can get quantitative .
Its just you know there's a certain sort of interaction in universe . How ? Newton's third law . You see that the object creating that interaction and the object which interacts will produce the interaction for the source object .
So now you defined quantities like inertial mass , velocity,distance , time . And using those you tried to figure as what quantitative effects these interactions produce . So for that in your experiments , you say that there are certain mathematical formulas/quantities that change due to these interactions , like Kinetic Energy and Momentum and Angular Momentum and then you used more mathematics to express how they change which led us to define more quantities such as force in terms of quantities we know like velocity,time etc.
So in the end these are just numbers defined through mathematical operations by us and somehow are cosmic or naturally existing , we don't know . But they help us to get quantitative of the observations we see .
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Kinetic energy is the energy involved when an object moves.The energy is the amount of force needed to move an object a certain distance (a Joule, the unit of energy is 1 Newton*1 metre).The momentum is the mass of an object multiplied by its velocity. The angular momentum of an object is a measure of how much force and time it would take to stop an object of a mass m from rotating, same as linear momentum would be the amount of force and time to stop an object moving in a straight line. Anyway, the momentum of the system is irrelevant, because what is important is that energy is never negative, because the quantity used in the equation is $mv^2$, not plain $v$.
