The metre Rule Pendulum

 Does the mass at the end of a pendulum affect its period? Many think it must—but it doesn’t. Using the @pascoscientific metre stick and rotary sensor, we see it’s all about length, not mass. So why no effect? Simple physics: mass cancels out in the equations.

Does the Mass of a Pendulum Matter? A Physics Myth Busted

If you've ever watched a heavy chandelier swinging gently in a church, or a child on a playground swing, you might have wondered: Does the weight at the end make it swing slower or faster?

This is one of the most commonly misunderstood ideas in physics—and one that many students (and even some teachers!) wrestle with. Surely a heavier mass must swing more slowly, right?

Let’s test it—and bust a myth using real data and good old Newtonian physics.

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The Common Misconception: Heavier Means Slower?

It's tempting to think that a heavier pendulum bob would take longer to swing back and forth. After all, heavier things fall more forcefully, don’t they? It’s true that heavier objects have more inertia—but they also have more weight pulling them down. So do these two factors cancel out?

That’s the key question. To find out, we ran a simple but precise experiment using a PASCO Scientific metre stick and a rotary motion sensor to track the swing of a pendulum accurately over time.

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The Experimental Setup

Here’s what we did:

1. Built a pendulum using a metre stick pivoted near one end.

2. Attached different masses at the end—ranging from a few grams to over 1kg.

3. Used a PASCO rotary motion sensor to track the angular displacement over time.

4. Measured the period—the time it takes to complete one full swing—for each mass.

5. Repeated the measurements with identical lengths but different masses.

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The Result? Mass Doesn’t Matter!

Surprise (or not): the period stayed the same regardless of the mass added at the end of the pendulum.

Even with a big, chunky 1kg weight or a light 50g bob, the time it took to swing back and forth didn’t change—as long as the length of the pendulum stayed constant.

Here's why:

The formula for the period of a simple pendulum (assuming small angles) is:

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Where:

• $\mathrm{T <span\; style="font-family:\; arial;">is\; the\; period</span>}$

• $L$ is the length of the pendulum.

• $g$ is the gravitational acceleration (about 9.81 m/s²)

Notice anything missing? That’s right—mass isn’t in the equation.

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Why Doesn't Mass Affect the Period?

It all comes down to Newton’s second law: $F = ma$.

• Heavier masses have more inertia (they’re harder to accelerate).

• But they also experience greater gravitational force (they’re pulled down more strongly).

These two effects perfectly cancel out in the pendulum system. The result? Mass makes no difference to the time it takes to swing.

This is the same principle Galileo famously demonstrated when (allegedly) dropping different weights from the Leaning Tower of Pisa. Whether legend or truth, the physics holds up: gravity pulls everything equally, regardless of mass.

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So What Does Affect the Period?

Two things:

1. Length of the pendulum – A longer pendulum has a longer period. It swings more slowly.

2. Acceleration due to gravity – On the Moon, the same pendulum would swing more slowly because gravity is weaker.

That’s it. Mass, shape, material (within reason), and size of the bob make no difference.

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Classroom Tips and Teaching Ideas

• Set up the experiment with students using different masses but the same string length.

• Use a stopwatch for rough measurements or a motion sensor for precision.

• Challenge students to predict what will happen before the experiment.

• Follow up by plotting mass vs. period—a flat line reveals a powerful lesson.

This is a great topic for introducing experimental design, data analysis, and thinking critically about intuition versus evidence.

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Final Thought: Let Physics Speak

In a world where misconceptions are common, it's satisfying to let a simple swinging object reveal one of the deeper truths of motion. Physics isn't about what seems right—it's about what can be measured, modelled, and proven.

So next time someone insists a heavier pendulum swings slower, just smile—and hand them a metre stick.