Levers and torque balance
How can a smaller force balance a larger force?
Change force and perpendicular distance from the pivot, then use torque to predict which side wins.
Learning goals
- Calculate torque using τ = F × d⊥.
- Compare opposing torques on the two sides of a pivot.
- Predict balance or turning direction from torque.
Before you begin
- Multiply decimals and recognise newtons (N) and metres (m).
- Know that a force can turn an object about a pivot.
Lever torque experiment
- 1Equal arms
- 2Change an arm
- 3Torque balance
- 4Reverse outcome
Observe, then explain
Work through four steps. Each button moves the interactive model to the matching observation state.
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With equal arms, the larger perpendicular force produces the larger torque.
Your task: Compare 30 N and 20 N at 1.0 m.
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Torque is force multiplied by the perpendicular distance from the pivot to the force's line of action. Doubling that distance doubles torque for the same force.
Your task: Move the smaller force farther out until it can balance the larger force.
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When clockwise and anticlockwise torques are equal, net torque is zero. The model shows a level beam, but this alone does not guarantee zero translational force.
Your task: Make 30 N × 0.8 m equal 20 N × 1.2 m.
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Changing either a force or an arm can change the sign of net torque and reverse the predicted turning direction.
Your task: Make the right torque larger and explain the direction from the numbers.
Build an explanation
Why perpendicular distance?
The turning effect uses the shortest distance from the pivot to the force's line of action. If force is not perpendicular to the lever, the along-beam distance is not automatically the moment arm.
The balance condition
In this two-dimensional model the left and right torques oppose. Equal magnitudes give zero net torque; otherwise the larger torque sets the qualitative tendency.
Mechanical advantage is not free energy
A longer arm can produce the same torque with less force, but its point of application usually moves farther. An ideal lever does not create energy.
Check your understanding
Printable worksheet
Complete the worksheet first. Answers and explanations are on a separate page.
Physics
Levers and torque balance
How can a smaller force balance a larger force?
- A perpendicular 20 N force acts 1.5 m from a pivot. What is its torque magnitude?
A. 13.3 N·m B. 21.5 N·m C. 30 N·m
- A 40 N force is 0.5 m to the left. How far out must a 10 N force act on the right to balance it?
A. 0.2 m B. 2.0 m C. 4.0 m
- If a force is not perpendicular to a lever, what is d in τ = Fd?
A. Perpendicular distance from pivot to the line of action B. The whole lever length C. The force-arrow length
- What can be concluded when opposing torques have equal magnitude?
A. Net torque is zero B. No forces exist C. The lever must spin rapidly
Answer page
Levers and torque balance
- 30 N·m
τ = Fd⊥ = 20 × 1.5 = 30 N·m.
- 2.0 m
The left torque is 20 N·m, so 10 × d = 20 and d = 2.0 m.
- Perpendicular distance from pivot to the line of action
The moment arm is the shortest, perpendicular distance to the force's line of action.
- Net torque is zero
Opposing torques cancel. This establishes rotational balance, not necessarily zero net force.