A 4 N force is applied to a 0.5 m lever arm at an angle of 30° from the lever. What is the torque about the pivot?
A2.0 N·m
B1.0 N·m
C1.73 N·m
D0.5 N·m
τ = rF sinθ = (0.5)(4) sin(30°) = 2 × 0.5 = 1.0 N·m. The sin(30°) = 0.5 factor accounts for the fact that only the component of force perpendicular to the lever arm contributes to rotation.
Question 2 True / False
The torque produced by a force on an object depends on where you choose the pivot point.
TTrue
FFalse
Answer: True
Torque is always calculated relative to a specific axis of rotation. The same force can produce different torque values depending on which pivot you choose, because the moment arm (perpendicular distance from pivot to the line of action) changes. This is why problems always require you to specify the axis.
Question 3 Short Answer
A force is applied exactly along the length of a lever arm (θ = 0°). What torque does it produce, and why?
Think about your answer, then reveal below.
Model answer: Zero torque, because sin(0°) = 0. A force directed straight through the pivot creates no tendency to rotate the object.
τ = rF sinθ. When the force is parallel to the moment arm, its entire effect is to push along the lever — none of it acts perpendicular to produce rotation. The perpendicular component of the force is what causes angular acceleration, and that component is zero at θ = 0°.