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An interesting case of a sideways force is a weight on the end of a string (like the Biblical slingshot used by [[David]] against [[Goliath]]). While the weight is revolving around you, the string is pulling the weight toward you - but it never gets any closer! This is called a [[centripetal force|centripetal]], or center seeking, force.
An interesting case of a sideways force is a weight on the end of a string (like the Biblical slingshot used by [[David]] against [[Goliath]]). While the weight is revolving around you, the string is pulling the weight toward you - but it never gets any closer! This is called a [[centripetal force|centripetal]], or center seeking, force.
=== Generalized momentum ===
The definition of momentum can be generalized in [[Lagrangian Dynamics|Lagrangian]] and [[Hamiltonian Dynamics|Hamiltonian]] dynamics, to
<math>
p=\frac{\partial L}{\partial \dot x}
</math>
where L is the [[Lagrangian]] and <math>\dot x</math> is the velocity. In some cases the generalized momentum is the same as the momentum defined above. For example, for a free particle the Lagrangian equals the [[kinetic energy]] and so
<math>
p=\frac{\partial (m\dot x^2/2)}{\partial \dot x}=m\dot x
</math>
as above.
[[Category:Physics]]
[[Category:Physics]]