Free · Physics models
Uniform Circular-Motion Force and Acceleration
Relate tangential speed, radius, rotation rate, inward force magnitude and circular acceleration.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A 2 kg mass moving at 3 m/s on a 1 m circle requires 18 N inward force and 9 m/s² acceleration.
F = mv²/r; a = v²/r; rotation frequency = v/(2πr). Displayed additive mass equivalent = m + F/g0.
Worked example
Enter these known values and leave the other values blank.
- Mass (m)
- 2 kg
- Radius (r)
- 1 m
- Tangential velocity (v)
- 3 m/s
- Rotation rate
- 28.65 rpm
- Force (F = mv²/r)
- 18 N
- Additive weight-equivalent mass
- 3.8355 kg
- Centrifugal acceleration (a)
- 9 m/s²
Assumptions and limitations
- This is uniform circular motion. The centripetal force points inward; an outward centrifugal force is a rotating-frame interpretation of the same magnitude.
- The rotation control stores cycles per second internally. RPM and rad/s are display conversions of that rate; angular speed in rad/s equals v/r.
- The additive mass equivalent m + F/g0 is a scalar comparison to weight, not a vector resultant of gravitational and centrifugal acceleration. It does not represent actual mass growth.
- Positive force and rotation are retained. Radius and mass are positive, and zero-motion boundary cases do not have every inverse.
- Enter known quantities and leave the unknown blank. Editable quantities support inverse solutions and locks; inconsistent locked quantities are reported. Unit selectors convert the quantity independently of its display.
Common questions
What is the difference between Hz and radians per second?
Hz counts complete turns per second; angular speed in radians per second is 2π times that count.
Does the equivalent mass increase the actual mass?
No. It compares an additive force magnitude with a weight scale and does not describe mass growth or a vector resultant.
How do I use the inverse calculation?
Clear the quantity you want to find and enter the remaining known values in their selected units. The model can only solve branches with enough independent information.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.