What is the formula for extending lever length to achieve the specified torque?

What is the formula for extending lever length to achieve the specified torque?

• A. TA = TW x L / TW x A
• B. TA = TW x A / L
• C. TA = TW / (L x A)
• D. TA = (TW + L) x A

Answer: (A)

Torque from a lever scales with the lever length: if you keep the same applying force, increasing the lever length increases the torque in proportion to the length ratio. So, to get the desired torque TA with a lever length L when the torque TW was set at the original length A, you multiply by the ratio L divided by A. The correct expression is TA = TW × (L / A). This captures the linear relationship between lever length and torque: doubling the length doubles the torque, keeping the setting consistent with the lever system. If you see the form that cancels TW (like (TW × L) / (TW × A)), you end up with L/A and lose the actual torque setting TW, which isn’t correct when a specific torque is required. A form like TW × A / L would imply torque goes up as the lever gets shorter, which contradicts how lever arms work. Using TW / (L × A) or (TW + L) × A mixes quantities in ways that don’t reflect the simple proportional change with lever length. A quick check helps: if the new length equals the original length, TA should equal TW; the correct formula satisfies this, while the others do not.

Torque from a lever scales with the lever length: if you keep the same applying force, increasing the lever length increases the torque in proportion to the length ratio. So, to get the desired torque TA with a lever length L when the torque TW was set at the original length A, you multiply by the ratio L divided by A. The correct expression is TA = TW × (L / A). This captures the linear relationship between lever length and torque: doubling the length doubles the torque, keeping the setting consistent with the lever system.

If you see the form that cancels TW (like (TW × L) / (TW × A)), you end up with L/A and lose the actual torque setting TW, which isn’t correct when a specific torque is required. A form like TW × A / L would imply torque goes up as the lever gets shorter, which contradicts how lever arms work. Using TW / (L × A) or (TW + L) × A mixes quantities in ways that don’t reflect the simple proportional change with lever length. A quick check helps: if the new length equals the original length, TA should equal TW; the correct formula satisfies this, while the others do not.