Torque

Why a long spanner beats a short one, and how a seesaw finds its balance. Place weights on a beam and see the torque — the turning effect of each, τ = m·g·d. Set the mass and distance on each side and the beam tips toward the larger torque, sitting level only when the moments match: mL·dL = mR·dR. A small mass far out can balance a big mass close in — the principle behind every lever. It all runs on your device.

You are in the Physics lab.

Trade mass for distance — a light weight far out balances a heavy weight close in.
Left moment—
Right moment—
Net torque—
Mechanical advantage—
Beam tilt—
State—

The two moments side by side: each bar is τ = m·g·d for that side. The beam sits level when the bars match; it tips toward the longer one.

Distance matters as much as force. The turning effect of a weight is τ = m·g·d — proportional to both the mass and how far it sits from the pivot. That is why 2 kg at 1 m exactly balances 1 kg at 2 m, and why moving a weight outward tips the beam even though its mass hasn't changed. Balance is not about equal weights; it is about equal moments. Trade mass for distance and the beam settles level the instant mL·dL = mR·dR.

Reading the simulation

What the two force arrows, the beam tilt and the moment bars are telling you.

1

Each weight pulls straight down

On each side a coloured arrow drops straight down from the weight — that is its weight force, W = m·g, labelled in newtons. Gravity always points down, so the arrow stays vertical even as the beam tilts. Its turning effect depends on how far out it acts: the lever distance dL or dR is marked under the beam in metres, and the moment printed beside each box, τ = m·g·d, multiplies the two together.

2

The beam tips toward the bigger moment

The beam pivots on the fulcrum and settles at an angle set by the net torque, τR − τL. When one moment is larger the beam rotates that way and the Beam tilt readout shows the angle and direction; when the two moments match the net torque is zero and it sits level. The State badge reads Balanced, Tips left or Tips right to name what you are seeing.

3

Balance means equal moments, not equal mass

The bar chart under the beam draws the two moments side by side. Balance is reached when the bars are the same length — that is mL·dL = mR·dR, with g cancelling from both sides. Because distance counts as much as mass, a small weight far out balances a big weight close in. The Mechanical advantage readout is the lever-arm ratio dL/dR — how much the longer arm multiplies a force.

How It Works

A force, a distance, and the principle of moments that ties them together.

1

Torque = force × distance

Torque, or moment, is the turning effect of a force about a pivot: τ = F·d. For a hanging weight the force is its weight m·g, so τ = m·g·d. Apply the same force further from the pivot and the torque grows — the reason a longer wrench turns a stubborn bolt a short one cannot. Slide a weight outward and its moment rises even though its mass has not changed.

2

The principle of moments

A beam is balanced — in rotational equilibrium — when the anticlockwise moment equals the clockwise moment. With one weight per side that is mL·dL = mR·dR, and g cancels out. Because distance matters as much as mass, a light mass far from the pivot can hold up a heavy mass close to it — exactly what the Seesaw preset shows.

3

Levers and mechanical advantage

That trade-off is how a lever multiplies force: apply a modest effort far from the pivot to lift a large load near it, with mechanical advantage deffort/dload. Seesaws, wheelbarrows, crowbars and cranes all run on the same τ = F·d you are adjusting here — set the masses and distances and watch the beam find equilibrium.

What is torque?
Torque (a moment) is the turning effect of a force about a pivot. For a force F at perpendicular distance d, τ = F·d; for a weight, τ = m·g·d. The further out the force acts, the larger the torque — which is why a long spanner loosens a bolt a short one cannot. This simulator shows the torque from each weight on a balance beam.
When does a balance beam or lever balance?
When the total anticlockwise torque equals the total clockwise torque — the principle of moments. For one weight each side, mL·dL = mR·dR (g cancels). So a small mass far from the pivot can balance a large mass close to it: 2 kg at 1 m balances 1 kg at 2 m. The beam sits level exactly when the torques match.
What is the difference between torque and force?
A force is a straight-line push or pull; torque is its turning effect about a chosen pivot. The same force gives different torques depending on where it acts: zero if it passes through the pivot, more the further away it acts. Torque changes rotational motion the way force changes linear motion — hence τ = I·α, the rotational Newton's second law.
How does this relate to levers and simple machines?
A lever is the balance beam put to work: because torque depends on distance, a force far from the pivot can lift a much larger load close to it, with mechanical advantage deffort/dload. Levers, wrenches, seesaws, wheelbarrows and cranes all run on the same τ = F·d you are adjusting here.

Teaching moments or simple machines? You can embed this simulator on your own site free — one line of code, no sign-up.

Classroom activity

A ready-to-assign lab using the simulation above. Free to use — nothing to install or sign up for, and no student data leaves the browser.

High school, College10–20 minInteractive simulation

Learning objectives

  • Compute torque from force and lever arm.
  • Apply the condition for rotational equilibrium.
  • Explain the role of the angle between force and arm.

Variables to change

  • Force magnitude
  • Distance from pivot
  • Angle of force

Procedure

  1. Apply a force at a set distance from the pivot and note the torque.
  2. Move the force farther from the pivot and observe the torque.
  3. Change the angle of the applied force toward parallel with the arm.
  4. Balance two torques on opposite sides of the pivot.

Observations

Record torque versus distance and angle, and the condition when the system balances.

Questions

  1. Write the torque equation.
  2. How does moving the force farther from the pivot affect torque?
  3. At what angle does a force produce maximum torque? Zero torque?
  4. State the condition for rotational equilibrium.
  5. Why is a door handle placed far from the hinges?

Explanation

Torque τ = rF·sinθ measures a force’s turning effect; it grows with lever arm and is largest when the force is perpendicular. A body is in rotational equilibrium when opposing torques balance to zero.

Answer key (for instructors)
  • 1. τ = r·F·sinθ, where θ is the angle between the force and the lever arm.
  • 2. Torque increases in proportion to the distance (lever arm).
  • 3. Maximum at 90° (perpendicular); zero at 0°/180° (along the arm).
  • 4. The sum of clockwise torques equals the sum of counterclockwise torques (net torque = 0).
  • 5. A longer lever arm gives more torque for the same push, making the door easier to open.

Educators: link or embed this simulation freely in your LMS or course guide.

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