# Does kinetic energy depend on reference frame?

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Ok, so the kinetic energy of an object is supposed to be proportional to the mass of the object, and to the square of the speed of the object, and speed is basically the magnitude of velocity, right?

Also, velocity depends on the reference frame in which it is measured, so long as said reference frame is also of a constant velocity, right?

So if we were considering a moving object from two reference frames, one that treats the object itself as a reference frame, and an external reference frame, from which the object was moving... would that imply different kinetic energies?

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Yes. The amount of kinetic energy depends on your reference frame. When we say energy is conserved, that applies within a reference frame. A quantity that stays the same between frames is invariant. Mass, for example, is invariant. Kinetic energy is not.

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Yes. The amount of kinetic energy depends on your reference frame. When we say energy is conserved, that applies within a reference frame. A quantity that stays the same between frames is invariant. Mass, for example, is invariant. Kinetic energy is not.

Interesting... so kinetic energy varies, depending on the reference frame one is referring to... so it has "kinetic energy with respect to x reference frame"?

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Imagine a universe in which all that exists are three balls(one red, one blue, and one yellow). Each ball has a mass of 1kg. The red and blue balls are at rest with respect to each other, but are moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball and the blue ball are moving and thus have kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball at rest relative to the blue ball, so has no kinetic energy(and neither does the blue ball). The yellow ball, however, is moving and thus has kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball. Thus energy is dependent on the reference frame and is not conserved from frame to frame. Mass, however is the same in every frame of reference. If we consider the three balls as a system and use the same reference frames, we get different values for the total energy of the system.

As stated, each ball has a mass of 1kg. In the reference frame where the red and blue balls are at rest, the yellow ball is observed to be moving at 100m/s with respect to the red and blue balls. In the reference frame where the yellow ball is at rest, the red and blue balls are each observed to be traveling at 100m/s with respect to the yellow ball.

How much KE does this universe have?

While energy is conserved in a frame of reference, it is not invariant between reference frames.

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Interesting... so kinetic energy varies, depending on the reference frame one is referring to... so it has "kinetic energy with respect to x reference frame"?

Yes, of course. A still body with respect to you may be moving with respect of a moving guy and may hit his head.

Edited by Bob_for_short
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No the body can have only one kinetic energy.

Imagine you are standing in a moving compartment with your friend, who has a ball. He throws the ball at you. Now with respect to a an obsever outside, it has

a velocity v. But because you are also moving with the compartment, the speed of the ball appears to you as v-speed of train.

[imath]K=\frac{1}{2} mv^2[/imath].

the velocities with repect to you and the observer outside are different , so the kinetic energy apparently has different values

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