How does pivot position change a hanging Technic-style beam’s return?

Moving the pivot changes the distance between the pivot and a beam’s centre of mass. At the same small angle, equal hanging beams with different pivot holes can experience different gravity torque. Both tend to return toward hanging vertical when their centres of mass are below their pivots. That turning effect does not by itself tell you their speeds or swing periods.

Same beams, different reasons to return

Imagine two identical rulers hanging on separate hooks. One hangs from its end, the other from a hole nearer the middle. Their lengths have not changed, but gravity acts through different lever arms. Our new Pivot Position Bench makes that comparison with two independently swinging seven-hole beams. It has 24 compatible parts, eleven assembly steps and an estimated twenty-minute build time.

The yellow beam hangs from its first hole; the red beam hangs from its second. Their round holes turn independently on a shared supported axle. Four middle half bushes retain them in separate planes. The axle runs through two tall posts, eight hole spacings apart, with outside retainers preventing axial escape. Each post has two separated fixing points to the base blocks. The stationary stand supplies support; your fingers should not substitute for a missing bearing or spacer.

Brick Experiment Channel’s credited inverted-pendulum demonstration inspired the stability question. Its description and inspected final-result footage show an upright mechanism with a reaction wheel, sensors and feedback. It explains electronics and control tuning, but the inspected material does not provide complete part-by-part assembly instructions for its mechanical structure. Our original two-beam bench uses no controller or reaction wheel and does not recreate that machine. It explores the simpler gravity effect that active control must overcome when a centre of mass is above its pivot.

Find the centre, then the turning effect

The centre of mass is the point through which the combined effect of gravity can be represented. A perfectly symmetric, uniform seven-hole beam would put it halfway between the end holes, three hole spacings from either end. With an eight-millimetre hole pitch, the end-pivot distance would be 24 mm. Moving the pivot one hole inward would make it 16 mm. These are ideal geometric comparisons, not measured mass-distribution certificates for every compatible beam.

Gravity pulls downward. When a hanging beam tilts, its centre of mass shifts sideways and rises above its lowest position. The sideways offset gives gravity a turning effect called torque. At a chosen angle, its magnitude is mass times gravitational acceleration times pivot-to-centre distance times the sine of the angle. The direction tends to reduce the hanging beam’s angular offset. At equal mass and angle, 24 divided by 16 gives a torque ratio of 1.5.

This is not a speed contest. The two beams have different mass distributions about their pivots, so their resistance to angular acceleration also differs. Friction, release conditions and existing motion matter. A moving beam can pass through its lowest point even though gravity torque is zero exactly there. Stable balance means small displacements produce a tendency to return, not that motion instantly stops.

Predict the direction before changing the pivot

Use the lab below at ten degrees from hanging vertical. Predict whether gravity turns the beam toward zero angle, away from it, or supplies zero torque. Check your answer, then compare the two torque readouts. Change the chosen mass from twenty to ten grams: both torque values halve, while their ratio stays the same. These masses are adjustable teaching inputs, not weights we measured for the parts.

Now switch only the virtual orientation to upright. At the same ten-degree offset, the gravity torque sign reverses. An upright centre of mass sits above the pivot, and tilting lowers it. Gravity therefore increases the offset instead of correcting it. Exactly upright still has zero gravity torque, but a nearby disturbance reveals the unstable equilibrium. The creator’s motor-driven feedback responds to disturbances; our bench has none. Keep the physical beams hanging and use the online counterexample rather than trying to balance or invert the real stand.

The lab uses ideal rigid bodies and Earth-like gravity of 9.81 metres per second squared. It displays millinewton-metres of signed torque and millijoules of gravitational potential energy above the lowest centre-of-mass position. A minus sign describes direction under the diagram’s angle convention. It does not mean negative speed, lost mass or a measurement error. No animation delay, timed challenge or motor is needed to explore it.

A fair release observation

Place the complete model on a level table and hold the stationary frame. Confirm both beams swing independently without rubbing, and all spacers remain seated. Move one beam gently about ten degrees sideways, within the twenty-degree operating limit. Release without pushing. Record its initial tendency and whether it passes through the centre. Repeat three times for each beam, keeping the angle, viewing direction, table and release method the same.

We have not physically tested this model. These cells are blank so your observations remain separate from the ideal calculation. A different-looking return does not prove a torque ratio; a video of motion alone cannot measure torque without additional information. Do not force the beam, add weights or increase the release angle to make a preferred result appear. If either beam sticks or a post moves, stop and repair the support before comparing behavior.

Common mistakes and next experiments

• Both beams move together. They should turn independently in round holes. Check for rubbing spacers or an accidentally shared friction connection. The axle is their support, not a drive coupling.
• The stand twists. Check both fixing points on each post and the stacked base blocks. A moving support changes the experiment.
• The beam stops off centre. Friction can prevent a small gravity torque from moving it. Check seating and rubbing rather than claiming that gravity disappeared.
• More torque must mean faster swinging. Torque and speed are different quantities. The lab deliberately leaves timing out.

Open the free Pivot Position Bench instructions for the animated assembly and printable booklet. The Pendulum Metronome offers a separate bob-position timing challenge, while the Balance See-Saw compares loads on opposite sides of a pivot. Read Pendulums, Balance and Bushes to connect the movement with the supports. Browse the free catalogue when you are ready for another mechanism.