circular motion formulas and interpretation
Uniform circular motion continually changes velocity direction even when speed remains constant.
The calculator returns the main connected circular-motion quantities together.
How to use the circular motion calculator
- Choose a model: Select the physical relationship that matches the known values.
- Choose the unknown: Select the quantity you need to calculate.
- Enter values and units: Provide every requested measurement using consistent units.
- Calculate: Check the formula, converted result, sign, and units.
Formula and variables
Centripetal acceleration equals speed squared divided by circular radius.
ac = v²/r- ac — Centripetal acceleration
- Inward acceleration (m/s²)
- v — Speed
- Tangential speed (m/s)
- r — Radius
- Circular-path radius (m)
Circular path example
A 2 kg object travels at 10 m/s around a 5 m radius.
- Mass
- 2 kg
- Speed
- 10 m/s
- Radius
- 5 m
- ac = 10²/5 = 20 m/s²
- Fc = 2 × 20 = 40 N
Result: Acceleration is 20 m/s² and force is 40 N.
The required net inward force is 40 newtons.
Understanding your results
Interpreting the result
Doubling speed quadruples acceleration and centripetal force at fixed radius.
A sign indicates direction only when a consistent rotational sign convention is used.
Assumptions
- Rotation is evaluated about a specified axis.
- Inputs are converted through coherent SI units.
- The selected formula adequately represents the physical system.
Limitations
- The calculator does not simulate time-varying inputs.
- Vector directions and multiple axes must be resolved separately.
- Losses such as friction are not added unless represented in the entered net value.
Common mistakes
- Mixing RPM with radians per second.
- Using diameter instead of radius.
- Entering a zero divisor.
- Ignoring the direction represented by a negative value.
Practical use cases
Physics and education
Check rotational kinematics and dynamics exercises.
Machines and mechanisms
Estimate quantities for wheels, shafts, rotors, and rotating equipment.
Frequently asked questions
Why are radians used in rotational formulas?
Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.
Can the result be negative?
Yes. A negative value means the quantity points opposite the direction chosen as positive.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.