Compare force speed radius and mass in maintained circular motion
Make the three syllabus comparisons while keeping the specified other variables fixed.
Exam scope and assessment notes
Extended only (Supplement) · Physics 0625, 2026–2028, section 1.5.1. Use k = F/x within the proportional range, identify its limit on a load–extension graph, and apply F = ma to the resultant force on the chosen body. Circular motion is qualitative here: compare force, speed, radius and mass while preserving the specified fixed variables. The circular-force formula and an understanding of the elastic limit are not required by this section. Written practice is self-checked; cumulative assessment, supervised practical experience and human subject-teacher review remain pending.
Before you begin
- Describe an inward perpendicular force.
- Identify which variables a comparison holds constant.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which quantities stay fixed when comparing force with circular speed in the specified syllabus relationship?
What you will learn
- Compare circular force and speed at fixed mass and radius.
- Compare radius or required force with the appropriate fixed variables.
One comparison needs one stated set of controls
For maintained circular-motion states, increasing the inward force permits a greater speed when mass and radius stay fixed. Increasing force gives a smaller radius when mass and speed stay fixed. These are different comparisons: one fixes radius and the other fixes speed, so their conclusions cannot be swapped.
At fixed speed and radius, a greater mass requires a greater inward force to maintain the same circular motion. State the two fixed quantities beside each prediction. The syllabus asks for these qualitative relationships here; its circular-force formula is not required, and these statements do not justify saying a doubled force doubles speed.
Compare maintained states rather than inventing a transition
An inward force perpendicular to instantaneous velocity turns the motion. The statement about greater speed at fixed radius compares maintained circular states; it does not mean a bare instantaneous perpendicular-force increase must immediately increase speed in every unconstrained situation. The conditions of the comparison matter.
If mass, speed and radius all change, the single-variable comparisons alone may not determine the force change. Request or use the missing controlled conditions rather than announcing a trend from one number. Likewise a snapshot does not prove that a path remains circular without the required continuing force arrangement.
Pause and explain
At fixed mass and speed, the inward force increases. What happens to the maintained radius?
Worked example
Describe the effect of greater inward force for (i) fixed mass and radius, and (ii) fixed mass and speed; then compare required force for greater mass at fixed speed and radius.
Show the worked solution
- At fixed mass and radius, the maintained speed is greater.
- At fixed mass and speed, the maintained radius is smaller.
- At fixed speed and radius, greater mass needs greater inward force.
Answer Greater speed; smaller radius; greater required force, under the respective stated controls.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Greater inward force is used at fixed mass and radius. What qualitative change occurs between maintained circular states?
Give me a hint
Identify the variable allowed to change in this comparison.
Compare my reasoning
- Mass and radius are unchanged.
- The greater force corresponds to greater maintained speed.
- No numerical multiplication factor is stated by this qualitative rule.
Speed increases at fixed mass and radius.
Look for these in your work
- State the fixed variables.
- Avoid an unsupported numerical factor.
Predict the radius when force decreases at fixed mass and speed; then predict required force for greater mass at fixed speed and radius.
Give me a hint
Use the correct pair of controls for each separate case.
Compare my reasoning
- Less force at fixed mass and speed gives a larger radius.
- Greater mass at fixed speed and radius needs greater force.
- The first case varies radius; the second varies required force.
Radius increases; required force increases in the second case.
Look for these in your work
- Keep each set of controls separate.
- State both trends.
A student says doubling force must double speed, even though mass and radius also changed. Explain why the qualitative syllabus comparisons do not support that claim.
Give me a hint
Check both the missing fixed conditions and the unsupported factor.
Compare my reasoning
- The force–speed comparison requires fixed mass and radius.
- Those conditions are not met in the stated change.
- Even with them fixed, the qualitative trend alone does not supply a speed-doubling rule.
The controls changed, and an increase trend does not justify the claimed doubling factor.
Look for these in your work
- Identify the uncontrolled variables.
- Separate a trend from a quantitative factor.
Common mistakes
- Keep the correct two variables fixed.
- Qualitative trend does not imply a direct doubling rule.
- Do not infer a single-variable trend when all conditions change.
What can you explain now?
If force decreases while mass and speed remain fixed, what happens to the circular radius?
Compare with the explanation
The radius increases.
This reverses the stated relationship between inward force and radius at those fixed conditions.
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Make it stick
Write all three circular-motion comparisons with the fixed quantities beside each conclusion.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.