Separate force balance from torque balance

1. Frame the question

Add torques only after choosing one common axis. For a horizontal rigid body, an upward force to the left tends to rotate clockwise while an upward force to the right tends counterclockwise. Equal upward forces on unequal arms do not cancel their torques. Force components determine translational acceleration; force locations also matter for rotation.

2. Build the mechanism

Our ideal pivot passes through the center of mass and keeps that point fixed. The body weighs 60 N. Its upward reaction adapts to balance the two applied upward forces and weight, leaving zero net vertical force. Because the pivot reaction and weight act through the selected axis, neither adds torque about that axis. Their zero torque does not mean the forces are absent.

The applied left force acts at x=−1 m and the right force at x=+2 m. With counterclockwise positive, τnet=−Fleft×1+Fright×2. For the supplied constant inertia 6 kg m², angular acceleration is τnet/6. Zero torque preserves an existing angular velocity; it need not stop an already spinning body.

A pair of equal, opposite parallel forces separated in space can have zero net force but a nonzero turning effect: a couple. Conversely, a force whose line passes through the center of mass can accelerate translation without initiating rotation about the center. Static equilibrium requires both force and torque balance, while rotational equilibrium alone only demands constant angular velocity.

3. Work an example

With Fleft=12 N and Fright=6 N, torques are −12 and +12 N m. The ideal pivot reaction is 60−18=42 N upward; both the net force and net torque vanish. Changing the left force to 6 N keeps net force zero through a 48 N pivot reaction, but leaves +6 N m net torque and α=1 rad/s².

4. Predict and investigate

Predict first: If net force is zero, must every point of an extended body have constant velocity?

Find three pairs that give zero net torque. Then hold the right force fixed and change only the left force. Draw all four forces, including weight and pivot reaction, and explain how net force stays zero while angular acceleration changes. Retain settings and raw evidence in the lesson notebook.

5. Transfer and explain

Try a new practice case

An upward 8 N force acts at x=−1 m and an upward 6 N force at x=+2 m. Find signed net torque, counterclockwise positive.

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

How could two forces produce zero net force but nonzero torque? Draw their application points rather than just two arrows at one dot.

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; 5.5; 5.6. 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.