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Particles have gravitational potential energy due to its position in the gravitational field. Systems have potential energy. Ascribing the energy to a particle is incorrect. We say the particle has potential energy and not the Earth (the body doing the work). That is incorrect. The potential energy is a function of the system, specifically the ...

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Yes potentials are frame dependent. Let us take the electric and magnetic fields as an example. The electric field can be written as: $$\vec E=-\frac{1}{c} \frac{\partial \vec A}{\partial t}- \nabla \phi$$ Where $\vec A$ is a vector potential and $\phi$ a scalar potential. Like wise, the magnetic field can be written as: $$\vec B=\nabla \times \vec A$$ ...

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A conservative force is one whose done work depends only on the initial and final states of the body it acts on, the energy associated with which is the state's potential energy. An illustration: Gravity is a conservative force. So the work done by it is dependent on the initial and final states (in this case, height from the earth's surface) of the body ...

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Your question seems to arise from a problem in which there is both a conservative and a non-conservative force. When you say "PE" you must be referring to the PE of the conservative force (by definition there is no PE of a non-conservative force). The work done by the conservative force does not depend on the path. Therefore you can define the potential as ...

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The following diagram should give you some insight: The black dot is the center of mass. If the center of mass is below the center of curvature of the bottom, then when you tilt the doll the c.o.m. will be displaced relative to the point of contact with the surface such that there is a torque that will attempt to right the doll again. If you place the ...

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When working with potential energy in classical mechanics we always compare the difference in energy between different points. It's only this difference that matters and not the absolute value of the energy (which is not observable). We are therefore free to take the zero-point wherever we want. This is the difference between the two formulas: in the second ...

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As per the formal definition: the potential energy of a field $\mathbf{v}$ is any function $f$ such that $\mathbf{v} = - \textrm{grad} f$ anywhere in the domain of definition of $\mathbf{v}$ (or wherever it makes sense). According to the above if $f$ is a potential for the field $\mathbf{v}$ so is $f + c, c$ being any constant; therefore if a field admits ...

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