Difference between revisions of "Forest UCM Energy CurlFcons"
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=Definition of curl= | =Definition of curl= | ||
| − | + | We have seen that the gradient operator is defined in cartesian coordinates as | |
:<math>\vec \nabla = \frac{\partial}{\partial x} \hat i +\frac{\partial}{\partial y} \hat j +\frac{\partial}{\partial z} \hat k</math> | :<math>\vec \nabla = \frac{\partial}{\partial x} \hat i +\frac{\partial}{\partial y} \hat j +\frac{\partial}{\partial z} \hat k</math> | ||
| + | |||
| + | can be used to find the function form of a conservative force given its potential energy | ||
[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]] | [[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]] | ||
Revision as of 23:09, 23 September 2014
A force with a curl of zero is a conservative force.
Thus taking the curl of the force is an easier way to test for conservative forces rather than calculating the work and inspecting to see if it only depends on the endpoints of the motion.
Definition of curl
We have seen that the gradient operator is defined in cartesian coordinates as
can be used to find the function form of a conservative force given its potential energy