Locate the force before calculating its torque

1. Frame the question

A force diagram for rotation must retain where each force acts. Replacing an extended body by a dot loses the distance and orientation needed to calculate turning effects. Mark the rotation axis, the point of application and the force’s line of action. The position vector runs outward from the chosen axis to the application point.

2. Build the mechanism

The turning-effect magnitude is τ=rF sinφ, where φ is the angle between that outward position vector and the force. Equivalently, τ=Fℓ, with ℓ the perpendicular distance from the axis to the force’s entire line of action. Radius and lever arm are equal only when the force is perpendicular to the radius. A large radial force can have zero torque.

For planar problems, classify each tendency as clockwise or counterclockwise about the named axis and assign opposite signs. This convention adds turning effects without requiring the three-dimensional vector direction of torque. The units are N m; although these match energy dimensionally, torque is not itself work. A force can exert torque before any angular displacement has occurred.

Changing the pivot changes the radius and can change the torque of a given force. Moving a force along its existing line of action leaves its torque about a fixed pivot unchanged, provided the same force and line are retained. That observation does not license replacing all forces by one arbitrary resultant at the body’s center.

3. Work an example

A 10 N force acts 0.4 m to the right of a pivot at 30° above the outward radius. Its upward component is 5 N, its lever arm is 0.4 sin30°=0.2 m, and its counterclockwise torque is 2 N m. At 150° the horizontal component reverses but the upward component and torque remain the same.

4. Predict and investigate

Predict first: Can equal force magnitudes at the same radius produce different torques? Can a nonzero force produce none?

Compare 0°, 30°, 90° and 150° at r=0.4 m. Sketch the force at the application point, extend its line of action and mark the perpendicular lever arm. Verify one calculation using Fℓ and another using rF sinφ. Retain settings and raw evidence in the lesson notebook.

5. Transfer and explain

Try a new practice case

A 12 N force is perpendicular to a 0.25 m radius. Find its torque magnitude.

Your numerical result (N m) Check number

Reveal worked check (practice, not mastery)

This extra practice is not saved and does not award mastery. Record your first answer, explanation and whether you revealed help in the lesson notebook. Use the lesson’s saved question separately.

6. Reflect and retain evidence

If a force acts through the axis but the application point is far away, why does using the application distance alone give a wrong turning effect?

Retain your first response, an extended-body diagram or labeled graph, units, assumptions and a changed-case prediction. Public worked checks are practice, not independent mastery evidence. Synthetic model captures are not a performed physical experiment.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 5 topic mapping: 5.3. Checked 30 October 2026. Planar clockwise/counterclockwise analysis; supplied formulas for extended bodies, no required calculus or three-dimensional torque-vector direction. Framework cross-reference, not AP authorization.