Mechanics
Unequal lever
A 50 N push on the 2 m arm balances a 100 N push on the 1 m arm — equal torques (τ = r × F) from unequal forces. Change one force in the Properties panel to see it tip.
Unequal lever — interactive Mechanics simulation. A 50 N push at 2 m balances 100 N at 1 m from a centered pivot: equal torques (τ = r × F) from unequal forces.
Torque and levers
A lever balances when the torques on both sides of the pivot are equal — forces on a shorter arm must be larger to match a longer arm.
Torque τ = r × F depends on both force and lever arm. With the pivot centered, a 50 N force 2 m from the pivot balances a 100 N force 1 m from the pivot: 50 × 2 = 100 × 1.
- τ = rF sin θ
- Στ = 0 at equilibrium
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
This lever's pivot is centered, just like the classic lever — but the right force is applied only 1 m from the pivot while the left force is 2 m away. If a 50 N push at the 2 m distance is balanced by a push at the 1 m distance, is that force bigger, the same, or smaller than 50 N?
Predictions to weigh
- It is bigger than 50 N
- It is the same — 50 N
- It is smaller than 50 N
Variable roles
What you set:
- Left Force (N)
- Right Force (N)
What you measure:
- Net Torque (from sim) (N·m)
- τ = r × F (calculated) (N·m)
How the investigation runs
- Open the Unequal Lever preset. A rigid beam is pinned at its exact center, like the classic lever — but the two downward forces are applied at different distances: 2 m on the left, 1 m on the right. A 50 N downward force pushes at the 2 m mark.
- Click the left force arrow on the beam and note its strength in the Properties panel, then click the right force arrow and do the same. Notice the two arms are different lengths.
- For each row below, set the left and right force strengths in the Properties panel to match, run the simulation, select the beam, and read the τ = r × F torque value from the Math panel.
Governing equation
Torque — τ = r × F
Torque is the turning effect of a force about a pivot: τ = r × F, where r is the distance from the pivot to where the force acts. With unequal arms, equal torques need unequal forces — a 50 N force 2 m from the pivot balances a 100 N force 1 m away, because both make 100 N·m.
What the printable worksheet asks students to work out
- For each row, calculate 1 m × Right Force − 2 m × Left Force by hand. Compare it to the net torque you read from the sim's Math panel. Do they match?
- In row 1 the 50 N push on the 2 m arm balances the 100 N push on the 1 m arm — different forces, equal torques. What must be true of a force and its distance from the pivot for a lever to balance?
Where this shows up beyond the lab
- A wheelbarrow is a lever too: your arms lift the handles about 2 m from the wheel (the pivot) while the load sits close to the wheel. If the load weighs 200 N and sits 0.5 m from the wheel, what upward force must you apply at the handles to balance it? What would you need if the load sat at the very end of the tray?
- A claw hammer pulling a nail, a crowbar, and a nutcracker are all levers with unequal arms. Pick one and identify its pivot, its applied force, and the load it moves — then explain why the short arm is the one on the load side.
- AP Physics 1 — Unit 5: Torque and Rotational Dynamics
- AP Physics C: Mechanics — Unit 5: Torque and Rotational Dynamics
- IB Physics — A.4 Rigid body mechanics
- General High School Physics — Rotation, gravitation & orbits
- NGSS High School Physics — Forces and Newton's second law
- Welcome to Unequal Lever
- Select the lever
- Press Play
- Unequal arms, equal torques
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.