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2. The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d<sub>i</sub> = d<sub>f</sub>) = 0) is zero.
2. The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d<sub>i</sub> = d<sub>f</sub>) = 0) is zero.
3. The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - grad U </math>.
3. The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
When the only forces present in a system are conservative, [[mechanical energy]] is conserved.
When the only forces present in a system are conservative, [[mechanical energy]] is conserved.