Question

If all the forces shown below have the same magnitude, which one produces the greatest torque about the pivot point?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

Answer 2

Torque is calculated as $\tau = rF\sin\theta$, where $r$ is the lever arm, $F$ is the force magnitude, and $\theta$ is the angle between the lever arm and the force. All forces have the same magnitude $F$. To maximize torque, we need to maximize $r$ and $\sin\theta$. In figures 1 and 2, the force is applied perpendicular to the lever arm, so $\sin\theta = 1$. In figures 3 and 4, the angle $\theta$ is less than 90 degrees, so $\sin\theta < 1$. Visually comparing figures 1 and 2, the lever arm in figure 2 appears to be longer than in figure 1. Therefore, figure 2 produces the greatest torque.