Physics 12 · Circular Motion Studio

Safety and scientific scope

For uniform circular motion, inward acceleration magnitude a_c=v²/r and net radial force requirement F_c=mv²/r. The arrows point tangent and inward, respectively. 'Centripetal force' is a description of the net inward force supplied by real agents; do not add it as an extra arrow on a free-body diagram already accounting for the actual inward forces.

1. Choose parameters and predict

If radius doubles or speed doubles, how will the net inward force change?

Mass 2 kg

Tangential speed 4 m/s

Circle radius 8 m

Illustrative flat-surface static μ_s 0.4

Position around path 0°

Import JSON

2. Position, velocity and inward acceleration

Teal: tangential velocityOrange: radial accelerationBlue: circular path

Vector lengths are indicative; velocity and acceleration have different units. Changing the phase shows the directions rotating at fixed speed, and does not change their magnitude.

Calculated model components (not measured)
Quantity	X component	Y component	Unit

3. Plot the square-speed relation

At fixed mass and radius, inward-force requirement is proportional to speed squared (including when the force-source capacity is inadequate).

Calculated inward force as speed changes (mass and radius held fixed)
Speed (m/s)	Required inward force (N)	Max lateral static-friction model (N)

4. Model evidence notebook

Locally saved synthetic circular-motion trials
#	Mass (kg)	Speed (m/s)	Radius (m)	μ_s	Required force (N)	Flat-road ideal constraint

My claim–evidence–reasoning and a limitation

Download mathematical circle-data CSV

5. Seven-Round Circular-Force Game

Seven different calculation problems drawn at random from eleven. Calculate F=m v²/r in newtons. This is an educational arithmetic model, not a real trajectory planner.

Start a new challenge.

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