Torque & Balance

The question behind the experiment

Balancing a meter stick is a test of turning effects, not a test of equal masses on each side. This course lets you compare hanging masses at different positions and explain why a smaller mass can balance a larger one. Identify the pivot before making a prediction. A mass's location matters because its force acts at a distance from that pivot. The investigation connects a visible balance result to a calculation of clockwise and counterclockwise torques.

Plan a useful comparison

Start with a centered pivot and keep the stick's geometry fixed. Move a hanging mass or change its amount, then predict which side will tip. Measure the distance from the pivot to the force's line of action rather than using the position marked from the end of the stick. Record the pivot coordinate separately from the hanging coordinate. Their difference is the relevant distance for a vertical hanging force, and a mistaken origin can produce a plausible-looking but incorrect balance calculation.

Connect the observation to the model

Compare force multiplied by perpendicular lever arm on each side. Opposite turning directions can cancel even when the force magnitudes differ. At the same time, translational equilibrium requires a force balance, including the support force. A force whose line of action passes through the pivot contributes no torque about that pivot, although it still acts on the stick. Show the forces at their actual points of application so the torque calculation can be checked against the free-body diagram.

Interpret the result carefully

The slanted-pull investigation shows why the lever arm is perpendicular to the line of action. Changing the pull angle changes the effective turning contribution for the same force magnitude. A force directed along the position vector does not turn the stick about the pivot. Compare the measured spring-scale pull with the angle and attachment point together. Using only the attachment distance would treat different force directions as equivalent and miss the geometric reason a larger pull may be needed.

Build an explanation from your evidence

Move the pivot away from the stick's center to investigate the stick's own weight. Its weight can now contribute a torque and must be included along with the hanging masses. Explain which terms change when the pivot moves, rather than carrying over a centered-pivot equation unchanged. Near balance, retain the position resolution and rounding of mass values. A slow tip still indicates an imbalance in the model, while an ideal equilibrium predicts cancellation of the summed turning effects.

A reference case from this course

In the centered-pivot reference, a 200 g mass at lever arm 0.20 m produces torque 0.3920000000 N·m. A 100 g mass at lever arm 0.40 m produces the same magnitude. Place those forces on opposite sides to compare cancellation; equal torque magnitude does not mean equal hanging mass.

Keep the investigation reproducible

Before changing the setup, write a prediction that names the measured quantity and the expected direction of change. Retain the original trial as a reference. Record the apparatus conditions, units, and whether you used Ideal or Real lab mode. If the selected activity includes seeded variation, keep the seed and run identity with the result so another comparison does not silently mix different conditions.

Separate the observation from its explanation. A reading or a counted object belongs in the evidence; the relationship you use to interpret it belongs in the reasoning. When a result differs from the reference case, check the settings and measurement procedure before deciding that the model relationship has failed. Describe a specific source of uncertainty and where it enters your calculation. Finish with a claim supported by the recorded comparison, and identify an additional trial that could distinguish your explanation from an alternative.

Continue the comparison

Compare the force accounting in Newton’s Second Law and radial motion in Circular Motion. Keep equilibrium and acceleration questions distinct when using a free-body diagram across these different apparatus arrangements.