Question

You are using a wrench to rotate a bolt around its center. Consider all the forces in (Figure 1), indicated by the arrows, to have the same magnitude. Which of the following scenarios apply zero torque? Select all that apply.

a) Scenario A
b) Scenario B
c) Scenario C
d) Scenario D
e) Scenario E

Answer 1

Scenarios B and C apply zero torque.

Step-by-step explanation:

Torque
`(\( \tau \))` is the rotational analog of force and is given by the equation
`\( \tau = r \cdot F \cdot \sin(\theta) \)`, where (r) is the lever arm (distance from the axis to the point where force is applied), (F) is the force applied, and
`\( \theta \)` is the angle between the lever arm and the applied force. For zero torque, either the force or the lever arm (or both) must be zero.

In Scenario A, the force and lever arm are non-zero, resulting in non-zero torque. In Scenario D, although the force is applied perpendicular to the lever arm, the lever arm itself is non-zero, causing a non-zero torque. In Scenario E, the force is parallel to the lever arm, so the torque is also non-zero.

However, in Scenarios B and C, the force is applied directly along the lever arm (parallel or antiparallel), resulting in a zero value for the torque. In these cases, the angle
`\( \theta \)` becomes 0 or 180 degrees, and since
`\( \sin(0) = \sin(180) = 0 \)`, the torque becomes zero despite the non-zero force or lever arm.

Understanding the conditions for zero torque is essential in mechanics and engineering, especially when dealing with rotational motion and equilibrium.