I recently posted a question involving the law of the lever, and I realized I was unclear on what it meant. I understand that, for a lever to be balanced, the effort force times the effort arm must be equal to the resistance force times the resistance arm. However, does this mean that this equation won't hold true for unbalanced levers, and if so, what is an example in which a lever is unbalanced? Also, if the equation only holds up for balanced levers, can we only use it when referring to balanced levers? I know this question seems simple, but I am trying to grasp the basic concepts before moving on to more difficult ones.
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Yes the lever must be balanced. By this I mean unaccelerated. It must either be motionless or rotating with constant speed.
You can apply a force on one end of a lever only. The lever will start to spin faster and faster.
It is like pushing on a mass. If you push equally on both sides, the mass will stay still or move at a constant speed. If you push on one side, it will accelerate.
mmesser314
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historically the law of the lever relates to a balanced system. A more useful intuition is that the torque of a lever is proportional to $F\times L$ where L is the distance of the tangential force from the axis of rotation and if the sum of the torques is zero, the system is balanced and does not rotate. The corollary is that if the total torque is none-zero the system will rotate.
The law of the lever can fail is some situations such as the "right angled lever paradox" of relativity. The "virtual work theorem" is much more generally applicable and extends to pulley and gear systems and works even the relativistic case.
KDP
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