Torque and Static Equilibrium Worked Examples Cheatsheet and Study Guide

How to start a torque and static equilibrium problem without guessing

Worked examples are where torque and static equilibrium stops being recognizable vocabulary and starts becoming usable reasoning. Worked examples are useful because they expose the order of thought: identify the controlling condition, choose the right model or rule, and only then compute or conclude. (OpenStax University Physics Volume 1: Chapter 12 Introduction; OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

Treat every static-equilibrium problem as a two-test problem: translational balance and rotational balance. If you skip that order, even familiar formulas become fragile under slight wording changes. (OpenStax University Physics Volume 1: Chapter 12 Introduction; OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

Meter stick torque balance

Masses hang at different points on a beam and the question asks for the unknown mass that balances the system. The aim here is using a pivot choice to remove one support force from the torque equation. (OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium; OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

Choose the fulcrum as the pivot so the support force contributes no torque.
Write clockwise and counterclockwise torques with the correct lever arms for each mass and for the beam if needed.
Solve the torque balance, then return to force balance if the reaction force is also required.

This problem is ideal for learning why pivot choice is a genuine analytical tool. (OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium; OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

Ladder against a wall

A ladder rests in static equilibrium while a person stands on it, and the prompt asks for contact forces or safe positions. The aim here is how multiple forces at different locations create one translational and one rotational condition set. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

Draw every force explicitly, including the ladder’s own weight and the person’s weight.
Pick a pivot that simplifies one reaction force away from the torque equation.
Use the result together with horizontal and vertical force balance to solve the remaining unknowns.

The lesson is that extended objects demand geometry and force balance together. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

Decision table for recurring torque and static equilibrium problems

Problem type	First move	Key check	Typical payoff
Meter stick torque balance	Choose the fulcrum as the pivot so the support force contributes no torque.	Write clockwise and counterclockwise torques with the correct lever arms for each mass and for the beam if needed.	This problem is ideal for learning why pivot choice is a genuine analytical tool.
Ladder against a wall	Draw every force explicitly, including the ladder’s own weight and the person’s weight.	Pick a pivot that simplifies one reaction force away from the torque equation.	The lesson is that extended objects demand geometry and force balance together.

Patterns the worked examples were meant to teach

A rigid body at rest must satisfy the force condition and the torque condition at the same time. If one is violated, the body will translate, rotate, or both. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: Chapter 12 Introduction)

Torque is the rotational effect of a force about an axis or point. The same force can produce very different torques depending on where it acts and how its line of action relates to the pivot. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

Checking forces but forgetting torques is a common reason a solution feels right while still landing on the wrong conclusion. Always ask what would happen rotationally after force balance looks good. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

Continue through the torque and static equilibrium cluster

Open torque and static equilibrium Overview when you want the broad conceptual map before diving back into detail.
Open torque and static equilibrium Exam Essentials when you want the highest-yield version of the same topic under time pressure.
This is the page you are already on, so use the note below it as your benchmark for what that variant should deliver.
Open torque and static equilibrium Revision Checklist when you want a memory audit instead of another long explanation.
Open torque and static equilibrium Common Mistakes when you want to debug the predictable traps that keep appearing in your answers.

Physics pages that reinforce this worked examples

photoelectric effect and the photon model Worked Examples is the nearest same-variant page if you want a comparable angle on a neighboring physics topic.
wave interference and diffraction Worked Examples is the next same-variant page if you want to keep the revision mode but change the content.
Browse the full physics cheatsheet archive if you want a broader subject sweep after this page.

Torque and static equilibrium FAQ for Worked Examples

What is the minimum condition for static equilibrium?

The net force and the net torque on the object must both be zero in the chosen inertial frame. If either condition fails, the object cannot remain statically balanced. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: Chapter 12 Introduction)

Why can I choose any pivot for torque balance?

Because the equilibrium condition for torques is valid about any axis or pivot. The smart move is to choose the one that simplifies the algebra. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

Why do teachers keep insisting on free-body diagrams?

Because torque depends on where forces act, not only on how large they are. A diagram keeps force location and direction visible at the same time. (OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

What is the most common mistake on torque problems?

Using the wrong lever arm or forgetting a force that acts through the object’s center of mass. Both mistakes come from an incomplete diagram. (OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

Source trail for torque and static equilibrium

OpenStax University Physics Volume 1: Chapter 12 Introduction was used for the static equilibrium requires zero linear and angular acceleration framing in this worked examples physics page.
OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium was used for the torque depends on force, lever arm, and chosen pivot framing in this worked examples physics page.
OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium was used for the free-body diagrams are not optional decoration framing in this worked examples physics page.

Extra consolidation for torque and static equilibrium

Treat every static-equilibrium problem as a two-test problem: translational balance and rotational balance. An object can pass one test and fail the other. A stronger final pass is to connect static equilibrium requires zero linear and angular acceleration to torque depends on force, lever arm, and chosen pivot and then force yourself to explain what changes between them instead of memorising each heading in isolation. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: Chapter 12 Introduction; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

A rigid body at rest must satisfy the force condition and the torque condition at the same time. If one is violated, the body will translate, rotate, or both. Torque is the rotational effect of a force about an axis or point. The same force can produce very different torques depending on where it acts and how its line of action relates to the pivot. Read those two ideas as one chain and notice how they control the way you would justify the topic in an exam, lab write-up, or data interpretation setting. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: Chapter 12 Introduction; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

To make that chain usable, walk the process through draw the body and forces and choose a pivot strategically. Include support forces, applied forces, and the object’s own weight at the correct locations. Pick the point that makes the torque equation simplest, often by eliminating one unknown reaction force. The point is not just to know the labels, but to know why this order reduces confusion when the prompt becomes more detailed or wordy. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

Masses hang at different points on a beam and the question asks for the unknown mass that balances the system. This problem is ideal for learning why pivot choice is a genuine analytical tool. Put that beside ladder against a wall and ask what stays stable across both examples even when the surface details change. That comparison work is usually where durable understanding starts to replace pattern-matching. (OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium; OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)

An object can have zero net force and still rotate if torques do not cancel. Always ask what would happen rotationally after force balance looks good. Once you can correct that error on purpose, look for using the wrong lever arm as the next likely point of failure so the topic gets cleaner with each pass instead of just feeling more familiar. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)

Quick recall prompts

Restate static equilibrium requires zero linear and angular acceleration in one sentence without leaning on the phrasing already used above. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: Chapter 12 Introduction)
Link that sentence to draw the body and forces so the topic feels like a sequence of moves instead of a loose list of facts. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)
Rehearse meter stick torque balance out loud and ask what evidence or condition you would check first. (OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium; OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)
Scan your next answer for checking forces but forgetting torques before you decide the response is finished. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium)
Compare this worked examples page with torque and static equilibrium Revision Checklist if you want the same content reframed for a different study task.

The lesson is that extended objects demand geometry and force balance together. If the topic still feels thin after that, move through the sibling and neighboring pages linked above and turn this page into the anchor note that keeps the whole cluster internally connected. (OpenStax University Physics Volume 1: 12.1 Conditions for Static Equilibrium; OpenStax University Physics Volume 1: 12.2 Examples of Static Equilibrium)