Calculate torque, beam equilibrium, and couples with a visual beam diagram. Perfect for GCSE and A-Level Physics.
Torque = Force x Perpendicular Distance
Quick Examples
Force times perpendicular distance from the pivot
When force is not perpendicular to the lever arm
At equilibrium, clockwise moments equal anticlockwise moments
Two equal, opposite forces separated by perpendicular distance d
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Torque (also called the moment of a force) is the turning effect of a force about a pivot point. It depends on two things: the magnitude of the force and the perpendicular distance from the line of action of the force to the pivot.
The Principle of Moments states: for a body in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point.
A couple consists of two equal and opposite forces whose lines of action do not coincide. A couple produces pure rotation — there is no resultant linear force.
Practice with these GCSE and A-Level style moments questions:
A child weighing 300 N sits 2 m from the pivot of a seesaw. Where should a second child weighing 400 N sit to balance the seesaw?
Principle of moments: CW moments = ACW moments
300 × 2 = 400 × d
600 = 400d
d = 600 / 400
d = 1.5 m from the pivot
A force of 15 N is applied to a door handle, 0.8 m from the hinges. Calculate the moment about the hinges.
τ = F × d
τ = 15 × 0.8
τ = 12 N m
A mechanic applies a force of 100 N to a 0.5 m wrench at 60° to the handle. Calculate the torque about the bolt.
τ = F × d × sin(θ)
τ = 100 × 0.5 × sin(60°)
τ = 100 × 0.5 × 0.8660
τ = 43.3 N m
A 4 m uniform beam is pivoted at its centre. A 50 N weight hangs 0.5 m from the left end, and a 30 N weight hangs 1 m from the right end. Where should a 20 N weight be placed to balance the beam?
Pivot at centre (2 m). Taking moments about the pivot:
CW: 50 × 1.5 = 75 N m
ACW: 30 × 1 + 20 × d = 30 + 20d N m
75 = 30 + 20d
20d = 45
d = 2.25 m from pivot (on the right side)
Avoid these frequent errors when solving torque and moments questions in GCSE and A-Level Physics exams:
The distance d must be the perpendicular distance from the line of action of the force to the pivot. If the force is at an angle, you need d × sin(θ) or use τ = Fd sin(θ).
Always check: is the force perpendicular to the lever arm? If not, use the sin(θ) formula.
Although N m and J have the same SI base units (kg m² s⁻²), torque and energy are different physical quantities. Examiners will mark you down for writing "J" instead of "N m" for torque.
Always write the unit as N m for torque. Reserve J for energy and work done.
Choosing a poor pivot point makes the problem harder. The best pivot eliminates an unknown force (distance = 0 means moment = 0).
Take moments about the point where an unknown force acts to eliminate it from the equation.
In A-Level problems, a uniform beam has its weight acting at its centre of gravity (the middle). Students often forget to include this when summing moments.
If the question mentions a "uniform beam of weight W", include W acting at the beam's midpoint.
The angle θ must be between the force vector and the lever arm, not between the force and the horizontal. Students often use the wrong angle.
Draw a diagram. θ is the angle between the force direction and the line from the pivot to where the force is applied.
Torque is the turning effect of a force about a pivot. It equals force times perpendicular distance: τ = Fd. The SI unit is N m. The further from the pivot and the larger the force, the greater the torque.
For a balanced (equilibrium) object: the total clockwise moments about any point equals the total anticlockwise moments. This lets you find unknown forces on beams and seesaws.
A larger distance d from the pivot (hinges) means a larger torque for the same force. Placing the handle far from the hinges makes it easier to open the door — you need less force.
A moment is the turning effect of a single force about a pivot. A couple is a pair of equal, opposite forces that produce pure rotation — the net force is zero but the net torque is not.
Zero torque occurs when: (1) the force is zero, (2) the distance from the pivot is zero, or (3) the force is parallel to the lever arm (θ = 0° or 180°, making sin(θ) = 0).
Choose a pivot, calculate CW and ACW moments (each = F × d), set them equal, and solve for the unknown. Choose the pivot where an unknown acts to simplify.
They have the same base units but represent different quantities. N m is for torque (turning effect), J is for energy. Never write "J" for torque in an exam.
Yes! It covers τ = Fd, τ = Fd sin(θ), principle of moments, equilibrium beam solving, and couples with step-by-step solutions. The Learn Mode guides you through each problem interactively.
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