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Re: [Phys-l] 'Torque' question

On 7/11/2010 8:33 PM, Fakhruddin, Hasan wrote:
Greetings folks!



Say a force is applied on an object to rotate it about a hinge. Why does it get easier (like needing less force) to rotate the object as the force is applied farther from the hinge?



~ Hasan Fakhruddin

Instructor of Physics

The Indiana Academy for Science, Mathematics, and Humanities

Ball State University
Other responders came at this question via energy considerations.
I propose to examine the force considerations, which may be closer to what you have in mind.

If a force is applied impulsively to a hinged object normal to the hinge direction, the resulting reactions vary with the distance of the bump from the hinge.
A bump directed to the center of mass will attempt to displace the
object in simple translation, which is frustrated by the hinge, which
restrains the translation at the hinge point with a force
in the opposite direction. A bump applied at the free edge induces a
hinge force directed in the same sense as the bump.

A position can be chosen to apply the bump which causes no hinge reaction. This is called the center of percussion. It occurs outboard of the center of mass. It can be visualized as the place at which all the object's mass would be concentrated, in order for the mass to move as a pendulum.

It is easy to see that the force applied at the hinge if any, is carried at the speed of sound from the point at which the object was bumped. So in order for the outboard edge to swing appropriately, the hinge force information now most travel to the free edge.
The normal force times its distance from the hinge is called the moment.

The idea of a center of percussion has some real applications, in terms of swung objects: golf clubs, tennis rackets, baseball bats, cricket bats. All these articles place most mass towards the free end, in order to place the center of percussion as close to the desired striking area as possible. The is sometimes called the sweet spot, though this is not quite accurate.

Brian W