How to Calculate Equivalent Torque Distance on a Pivoting Rod?

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To calculate the equivalent torque distance on a pivoting rod, the torque (t) is given by the equation t = rF, where r is the distance from the pivot to the point of force application. The proposed solution for the distance d, when the force F is applied at an angle theta, is d = Lsin(theta). This formula is valid as it accounts for the effective component of the force that contributes to torque. When the angle is 90 degrees, the force is fully effective in generating torque at that distance. The discussion confirms that the approach to finding d is correct for horizontal force application.
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Homework Statement



A rod can pivot at one end and is free to rotate without friction about a vertical axis. A force F is applied at the other end, at an angle theta to the rod. If F were to be applied perpendicular to the rod, at what distance d from the axis of rotation should it be applied in order to produce the same torque t?

Homework Equations



t = rF

The Attempt at a Solution



My answer: d = Lsin(theta).

Is that correct or am I missing something?
 
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If the force is applied horizontally this would be true.

When the angle is 90 degrees the force would be fully engaged in developing torque at that displacement.
 

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