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Old Apr 20th 2009, 09:03 AM   #1
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Central forces and torque

In rotational dynamics, it is said that central fores exert no torque on a system and therefore conserve angular momentum L . i.e. L = constant. This is because the force vector is directed along the radius vector. i.e. F parallel to r.

However there seems to be a contradiction. If the central force is exerting no torque why would the system rotate with an angular momentum?

For example if you have a two particles of opposite electric charge in an electric field forming a dipole, the central force, from the electric field, exerts a force on both particles to try and align the dipole with the field. Thus the dipole rotates and a torque has been exerted on the system.

Many thanks
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Old Apr 20th 2009, 11:32 AM   #2
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Suppose you first align the dipole and then switch on the field would there be any torque? NO because it is already aligned i.e. R and F are parallel. Thus the torque comes about because it is not aligned.

Again When a torque is applied it can cause rotation but just because there is rotation there need not be a torque. Let me explain with this example . Suppose a body is moving in a straight line at constant speed. DOes this imply a force is being applied? No from Newtons first law.
However when a force is applied it can cause motion. A net force can be definitely said to be present only when there is acceleration.
Similarly only when angular accln is present can we say there is a net torque. For circular motion all that is needed is an initial tangential velocity (note not force) and a centripetal accln.
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Old Apr 20th 2009, 12:31 PM   #3
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"Again When a torque is applied it can cause rotation"

Does this mean that in the attatched diagram the central force F from the electric field, E, can exert a torque to rotate the dipole from this starting position?

(note COM denotes centre of mass)
Attached Thumbnails
Central forces and torque-electric-field.jpg  

Last edited by Dynamo; Apr 20th 2009 at 12:34 PM.
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