Posted by: JJA (jjanagnost@att.net) on Sun May 29 09:15:25 2005

> >>> Strictly speaking, the definition of torque given in research10.html is not correct. It does not require forces in opposite direction for a body to rotate. For example, in your upper picture, you show two forces in the same direction and a "reaction". In that picture, you correctly note that the body does not rotate.
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> However, this is because the forces are applied at equal distances from the center of mass of the rectangle. This is why the body does not rotate. If you had used only one of the two force lines, say the top one but not the bottom one, the rectangle would initially rotate in a clockwise fashion. This is due to the torque that results from the upper force times the lever arm from the applied force to the center of mass of the object. <<<
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> Hi JJA
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> Strictly speaking, the definition of torque given in research10.html is exactly correct. You stated, “If you had used only one of the two force lines, say the top one but not the bottom one, the rectangle would initially rotate in a clockwise fashion. This is due to the torque that results from the upper force times the lever arm from the applied force to the center of mass of the object.”
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> In the example you cited, unless the line of force is directed at the center of mass, there are forces from opposing directions being applied. (1) The line of force you referred to. (2) The opposing force is the vectored inertia of the object. -- Example: If you apply a force with your finger to the center of a pencil lying on a table, it does not rotate about a vertical axis because the vectored opposing force on each side is balanced (sum = 0). However, if the force applied is off center, rotation is induced because the opposing vectored force of inertia (and friction in this case) is greater on one side than the other.
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> Note: It should also be pointed out that if the single force is directed in a straight line, the inducement for the object to rotate will cease once its length becomes tangent with the direction of force.
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> Jack Mankin

No, research10.html really isn't correct. Opposing forces are not required to produce torque. Please go to any standard college textbook (such as Beer and Johnston, 'Vector mechanics for engineers') and review the definition. Your definition is more consistent with the terms "pure moment" or "force couple" then the standard definition of torque.

In the example I cited, there are no opposing forces. The only force being applied to the rectangle is the upper force. ("Vectored inertia" is not a physics term).

However, I think I agree with your example of the pencil lying on the table. If you push on the pencil through its center of mass, the pencil will translate but not rotate. This isn't because of any opposing force (assuming a frictionless surface) but because you're pushing through the center of mass. If you push on the pencil at a point other than the center of mass, it will both rotate and translate.

Perhaps the confusion is the latter point. To cause a body to have pure rotation (and no translation) then opposing forces are required. Strictly speaking, however, this isn't how torque is defined. For example, in your lug nut example on research10.html, you use a 4 prong tire wrench to make your point. However, if you use a standard wrench you can unbolt the nut just fine by applying only a single force at a lever arm. Anyone will tell you that this method applies plenty of torque even though there is no opposing force being applied!

-JJA