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'''Conservative [[force]]s''' are those that possess certain properties:<ref>Serway and Beichner, ''Physics for Scientists and Engineers'', Fifth Edition</ref>
 
'''Conservative [[force]]s''' are those that possess certain properties:<ref>Serway and Beichner, ''Physics for Scientists and Engineers'', Fifth Edition</ref>
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# The [[work]] it does on a particle is independent of its [[trajectory]].
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* The [[work]] it does on a particle is independent of its [[trajectory]].
 
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* 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.
# 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.
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* The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
 
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* The [[curl]] of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>
# The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
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# The [[curl]] of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>
      
When the only forces present in a system are conservative, [[energy]] is conserved.
 
When the only forces present in a system are conservative, [[energy]] is conserved.
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