Definition: The moment (or torque) of a force is a measure of its ability to cause rotation about a pivot (fulcrum). It depends on the magnitude of the force, the distance from the pivot, and the angle between the force and the line joining the point of application to the pivot.
Mathematically, \$\tau = F \times d \times \sin\theta\$ where \$\tau\$ is the moment, \$F\$ is the magnitude of the force, \$d\$ is the perpendicular distance from the pivot to the line of action of the force, and \$\theta\$ is the angle between the force and the lever arm.
Key Points
The unit of moment in the SI system is newton‑metre (N·m).
If the line of action of the force passes through the pivot, \$d = 0\$ and the moment is zero – the force produces no turning effect.
Clockwise moments are usually taken as negative, anticlockwise as positive (or vice‑versa, as long as consistency is kept).
Everyday Examples
Opening a door: the force applied at the handle is far from the hinges, giving a large moment.
Using a wrench to loosen a bolt: increasing the length of the wrench increases the distance \$d\$, making it easier to turn the bolt.
Seesaw (teeter‑totter): the children’s weights act at different distances from the pivot; balance is achieved when the clockwise moments equal the anticlockwise moments.
Turning a steering wheel: the driver’s hands apply force at the rim, producing a large moment to rotate the wheel.
Using a crowbar to lift a heavy object: the longer the bar, the greater the moment for the same applied force.
Balancing Moments – The Principle of Moments
For an object to be in rotational equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments:
This principle is used in many practical situations, such as checking that a seesaw is level or that a beam is not rotating under load.
Sample Table: Calculating Moments
Force \$F\$ (N)
Perpendicular distance \$d\$ (m)
Angle \$\theta\$ (°)
Moment \$\tau\$ (N·m)
30
0.5
90
\$30 \times 0.5 \times \sin 90^\circ = 15\$
50
0.2
30
\$50 \times 0.2 \times \sin 30^\circ = 5\$
80
0.4
0
\$80 \times 0.4 \times \sin 0^\circ = 0\$
Suggested diagram: A lever with a pivot, showing two forces applied at different distances and angles, illustrating clockwise and anticlockwise moments.
Quick Check Questions
What happens to the moment if you double the distance \$d\$ while keeping the force unchanged?
A 10 N force is applied at the end of a 0.3 m wrench at an angle of 60°. Calculate the moment.
Explain why a longer crowbar makes it easier to lift a heavy object.
Summary
The moment of a force quantifies its turning effect: \$\tau = F d \sin\theta\$.
Both the magnitude of the force and its perpendicular distance from the pivot are crucial.
Everyday tools such as doors, wrenches, and seesaws illustrate the concept clearly.
Balancing moments is essential for rotational equilibrium.