# Energy dependence on observer framework

## Main Question or Discussion Point

Does mechanical energy of a system depend on the framework of an observer (neglecting a constant)?

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Nugatory
Mentor
Does mechanical energy of a system depend on the framework of an observer (neglecting a constant)?
Yes. The kinetic energy of a bullet is zero in the frame of an observer who is at rest relative to the bullet, non-zero for an observer who is at rest relative to the target of the bullet.

HallsofIvy
Homework Helper
I agree with Nugatory but I can't help but wonder what you mean by "neglecting a constant".

I agree with Nugatory but I can't help but wonder what you mean by "neglecting a constant".
Ok, Right. The statement "neglecting a constant" is my mistake.
I clarify my purpose of the question:
Newton's laws are only valid in inertial framework. I like to know whether energy formalism is valid in non-inertial framework or not? In other words, can one solve the problems exactly, using conservation of energy in non-inertial framework?

Ok, Right. The statement "neglecting a constant" is my mistake.
I clarify my purpose of the question:
Newton's laws are only valid in inertial framework. I like to know whether energy formalism is valid in non-inertial framework or not? In other words, can one solve the problems exactly, using conservation of energy in non-inertial framework?

$\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt = \frac{1}{2}m v^2(t_1) - \frac{1}{2}m v^2(t_0)$ is valid in frames where $\vec{F}(t) = m \frac{d\vec{v}(t)}{dt}$

That is, in inertial frames.

You still can use it in non-inertial frames IF you add "inertial forces".

$\int_{t_0}^{t_1}\vec{F}(t)\cdot\vec{v}(t)dt = U(x(t_0),y(t_0),z(t_0))- U(x(t_1),y(t_1),z(t_1))$ is valid in any frame where $\vec{F}(x,y,z) = -\nabla U(x,y,z)$

where $U(x,y,z)$ does not vary with time in this frame.

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