Force applied at centre of mass

Thread starter chandran
Start date Oct 4, 2007
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Applied Centre of mass Force Force applied Mass

AI Thread Summary

Applying a force at the center of mass results in pure translation without rotation. This is because torque, defined as the cross product of the position vector from the center of mass to the force application point and the force itself, becomes zero when the position vector is zero or parallel to the force. Consequently, no rotational force is generated. The mathematical proof hinges on the relationship between force, torque, and the center of mass. Understanding this principle is crucial in mechanics and dynamics.

Oct 4, 2007

chandran

If a force is applied at centre of mass the object will only translate and not rotate. Can anyone proove this mathematically?

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Oct 4, 2007

Zorodius

Torque is the cross product of the vector from the center of mass to the point where the force is applied (r), and the force. If r is zero, or r is parallel to the force, there will be no torque, and so no rotational force.

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