How this calculation works
Convert the selected speed to consistent linear and angular values, then calculate the required inward resultant. At zero speed there is no finite revolution period.
Inward acceleration = v²/r = ω²r; inward net force = mass × accelerationA worked example
A 3 kg object moving at 4 m/s around a 2 m radius requires 8 m/s² inward acceleration and a 24 N inward net force. Its angular speed is 2 rad/s and period is π seconds.
Good to know
Uniform circular motion, non-negative speed and a fixed radius. No tangential acceleration, banking, force-source identification or safe-speed/strength assessment.
Reference: Reference: model, definitions and assumptions (opens in a new tab) ↗
Changing direction requires acceleration even at constant speed
At the default 4 m/s around a 2 m radius, radial acceleration is 4²/2 = 8 m/s². Multiplying by the entered 3 kg gives a 24 N inward resultant. Constant speed refers to the size of velocity; its direction keeps changing around the circle.
That inward resultant must be supplied by the real forces in the problem. It might be tension, gravity, friction or a combination. Adding a new “centripetal force” after already summing those inward forces would count the same radial requirement twice.
The kinetic energy calculator also uses speed squared, but energy and an inward force requirement have different units and meanings.
Holding linear speed and holding RPM are different experiments
At fixed linear speed, doubling radius halves v²/r. At fixed RPM, doubling radius doubles linear speed and therefore doubles ω²r. These are different conditions, so apparently opposite radius comparisons can both be correct.
For a 2 m radius at 60 rpm, one revolution takes one second and angular speed is 2π rad/s. Linear speed is 4π m/s. The same numeric value entered as m/s would describe a different motion. The mode and unit selectors make that distinction explicit.
Read the squared-speed comparison without turning it into a safety rating
At the default radius and mass, halving speed from 4 to 2 m/s reduces required force from 24 to 6 N. Doubling speed to 8 m/s increases it to 96 N. The table keeps mass and radius unchanged so this squared relationship is visible.
Zero speed gives zero radial acceleration and zero required radial force, but there is no finite revolution period. The kinetic energy calculator also involves speed squared, while the friction force calculator addresses whether a supplied contact can provide a particular tangential force. Neither result establishes a safe structural load or safe vehicle speed.
A few questions, answered
Is centripetal force an extra physical force?
It names the required inward net force. The actual forces supplying it must be identified from the situation.
Why does twice the speed require four times the force?
At the same mass and radius, force is proportional to v². Squaring a factor of two gives four.
What happens at zero speed?
Radial acceleration and force are zero. A revolution period is not defined because no revolution occurs.
Are tangential acceleration and changing radius included?
No. This calculation uses uniform circular motion at a fixed radius and reports the radial requirement.