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eduKate Learning Manual: Circular Motion Practical Skills | Measuring Centripetal Force Without Letting Radius, Speed and Timing Drift Together

Wait, What? If the speed changes while you change radius, you are no longer testing radius.

Circular-motion practicals are easy to contaminate because force, speed and radius are tightly coupled. A student may move a marker outward, spin faster without noticing, and then attribute the larger force to radius alone. The experiment therefore lives or dies on variable control.

The model

For uniform circular motion:

F = mv²/r

or, using angular speed ω:

F = mω²r

These forms show why the independent variable must be chosen explicitly. Testing F against v² requires m and r to stay constant. Testing F against r at constant ω requires m and ω to stay constant.

Timing many revolutions

One revolution is usually too fast for reliable hand timing. Time 10, 20 or more revolutions, then divide by the count to obtain the period T.

Speed can then be estimated from:

v = 2πr/T

Reaction-time uncertainty becomes a smaller fraction of the total interval when many cycles are timed.

Radius must be measured to the centre of mass path

The relevant radius is the distance from the axis of rotation to the path of the rotating mass’s centre. Measuring to a string knot or outer edge can introduce a fixed geometry error.

A marker on the string helps maintain a chosen radius, but the marker itself is not necessarily the centre-of-mass location.

Using a hanging mass to set force

In one common design, a hanging mass provides string tension. If the hanging mass remains approximately stationary while the rotating mass moves in a horizontal circle, the string tension is close to the hanging weight:

F ≈ mhg

If the hanger bobs up and down, the tension is not simply constant weight. The apparatus itself is telling you that the intended force condition has failed.

Quantitative window

A 0.050 kg rotating mass moves in a circle of radius 0.40 m. Twenty revolutions take 16.0 s.

T = 16.0/20 = 0.800 s

v = 2π(0.40)/0.800 ≈ 3.14 m s⁻¹

F = mv²/r ≈ 0.050(3.14²)/0.40 ≈ 1.23 N

This corresponds to a hanging mass of about 0.125 kg if the simple tension model holds.

Graph methods

At fixed m and r, plot F against v². The model predicts a straight line with gradient m/r.

At fixed m and ω, plot F against r. The model predicts a straight line with gradient mω².

Choosing the wrong graph can hide whether the experiment actually tests the intended proportionality.

Observation versus inference

Observation: “At r = 0.40 m, 20 revolutions took 16.0 s while the hanger remained approximately stationary.”

Inference: “The rotating mass moved with approximately steady speed and experienced inward force near 1.23 N under the model assumptions.”

Failure modes

Unfamiliar transfer: banked motion

A car on a banked curve still needs inward acceleration, but the inward force can come from components of normal reaction and friction rather than string tension. The transferable skill is to identify the radial direction and determine which real forces contribute to the net inward force.

Secondary → JC → deeper Physics

Secondary: connect circular motion to inward acceleration and measure period reliably.

JC: test F ∝ v² and F ∝ r under controlled conditions, use graphs and analyse tension assumptions.

Deeper Physics: extend to rotating frames, angular momentum, rigid-body dynamics and non-uniform circular motion.

Checkpoint

A student doubles the radius and notices the required hanging mass also doubles, but the revolution time changes too. Has F ∝ r been demonstrated?

Answer key and WHY reasoning

Not cleanly. The F ∝ r form assumes angular speed is constant. If the period changed, ω changed too, so two variables influenced the force.

How to study this practical

Before each run write three quantities in a triangle: force, radius, speed. Circle the one you are changing and cross-check that the other two are truly controlled or explicitly measured.

Evidence boundaries

A school circular-motion experiment tests the radial-force model under approximately uniform speed and controlled geometry. It does not prove that string tension is perfectly constant or that the motion is exactly circular at every instant.

Authoritative next steps

Teaching Guide

Give students two datasets: one with radius varied at constant period and one with radius varied while period drifts. Ask which can test F ∝ r. This makes control-variable reasoning visible rather than implicit.

Explore the connected learning guides

Choose the question that brought you here. Open one useful guide, try a small task, and stop when you have what you need.

Take one question further

The same learning habit can travel across subjects, while each subject keeps its own methods. These routes help you notice a difficulty, understand one part of it, and return to something you can do.

A word is familiar, but using it is difficult.

Move from recognising a word to retrieving it in a new context. Understand vocabulary plateaus.

Try it without the guide: Choose one word you already know. Close the guide and use it in a new sentence. Explain why it fits; try another context tomorrow.

A piece of writing has ideas, but the reader loses the thread.

Make the order of events and the links between sentences clear. Explore composition writing.

Try it without the guide: Choose one short paragraph. Read the relevant explanation, close it, and revise the paragraph. Ask someone to tell you what happened and why.

The Mathematics seems familiar, but marks still disappear.

Find the first point where the working stops being reliable. Find Secondary 4 A-Math mark leakage.

Try it without the guide: For a Secondary 4 A-Math question you have attempted, locate the first uncertain line. Repair that step, then try a comparable question without the worked answer.

A Science fact is remembered, but the explanation is incomplete.

Connect the evidence to a scientific idea and the resulting change. Follow the Primary Science learning route.

Try it without the guide: Choose a familiar Primary Science example. Explain the evidence, the idea and the result without notes. Then change one condition and explain your prediction.

Two accounts of the world seem to disagree.

Check the question, source, date and evidence before combining claims. Explore the World Knowledge research library.

Try it without the guide: Take one claim. Find the source best placed to support it, note its date, and state what remains uncertain. Return to your original question.

There is plenty of help, but independence is hard to see.

Check what the learner can understand and do after support is removed. Understand how education works.

Try it without the guide: Choose one small task the child has practised. Agree on a calm, brief attempt without prompts. Use what happens to choose one next step, then stop.

For the structure behind these connections, read the eduKateSingapore runtime manifest and the eduKate ecosystem boot contract. The reader map describes public navigation; those manifests preserve the wider ownership and return rules.

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