A 100 N force is applied at point P, which is located 0.8 m from pivot O. However, the force's line of action passes directly through point O. What is the moment of this force about O?
A80 N·m, because moment = force × distance to point of application
B0 N·m, because the moment arm (perpendicular distance from O to the line of action) is zero
C100 N·m, because the full force magnitude creates rotation
DIt cannot be determined without knowing the force direction
When a force's line of action passes through the reference point, the perpendicular distance from the point to the line of action is zero, so M = F × d = 100 × 0 = 0. The distance to the point of application (0.8 m) is irrelevant — the moment arm is always the perpendicular distance from the pivot to the LINE OF ACTION, not to the application point. This is the most common error in moment calculations.
Question 2 Multiple Choice
A wrench handle is 0.4 m long and a 60 N force is applied at its tip at 30° to the handle. What is the correct moment arm to use when calculating the moment about the bolt at the other end?
A0.4 m — the distance from the bolt to where the force is applied
B0.4 × cos(30°) = 0.346 m — the component of the handle along the force direction
C0.4 × sin(30°) = 0.2 m — the perpendicular distance from the bolt to the force's line of action
D0.4 / sin(30°) = 0.8 m — the extended line of action length
The moment arm is the perpendicular distance from the pivot (bolt) to the force's line of action. When the force makes angle θ with the handle, the perpendicular distance is r × sin(θ) = 0.4 × sin(30°) = 0.2 m. So M = 60 × 0.2 = 12 N·m. Alternatively, using M = r × F with the cross product gives the same result: the cross product automatically extracts the perpendicular component.
Question 3 True / False
If you slide the point of force application along the force's line of action to a different location, the moment about any given reference point remains unchanged.
TTrue
FFalse
Answer: True
The moment depends only on the force magnitude and the perpendicular distance from the reference point to the LINE OF ACTION — not on where along that line the force is applied. The line of action extends infinitely in both directions; any point on it gives the same line, the same perpendicular distance to the pivot, and therefore the same moment. This principle (called the principle of transmissibility) is fundamental to rigid-body statics.
Question 4 True / False
The moment of a force about a point depends on the distance from the pivot to the specific point where the force is applied to the body.
TTrue
FFalse
Answer: False
This is the most common misconception in moment calculations. The moment depends on the perpendicular distance from the pivot to the force's LINE OF ACTION, not to the point of application. A force applied at the tip of a wrench versus halfway down the handle will have different moment arms only if moving the application point changes the line of action — and if the force direction stays the same, it usually does. The correct mental model is: extend the force into an infinite line, then measure the perpendicular from the pivot to that line.
Question 5 Short Answer
Why is the moment arm defined as the perpendicular distance from the reference point to the force's line of action, rather than simply the distance from the reference point to the point of force application?
Think about your answer, then reveal below.
Model answer: Rotation depends on how far 'off-center' the force is pushing — that is, what component of the force is acting tangentially rather than radially toward/away from the pivot. Only the perpendicular component creates rotation; a force aimed directly at (or away from) the pivot has zero rotational effect regardless of how far away the application point is. The moment arm captures this by measuring the perpendicular offset of the entire line of action from the pivot. The cross product M = r × F computes this automatically: the cross product of r and F extracts the perpendicular component, which equals F × d where d is the perpendicular distance to the line of action.
This also explains the zero-moment case: when the line of action passes through the pivot, there is no perpendicular offset and the force creates no rotation, no matter how large the force or how far away the application point. This fact is exploited constantly in equilibrium analysis to choose strategic reference points.