Rotating mechanisms—robotic arms, turntable-mounted actuators, CNC rotary tables—generate forces that static load calculations miss. This calculator lets you work out both the Coriolis force and centripetal force on a moving mass, using weight, radial velocity, angular velocity, and radius. If you're building anything with rotating links or arms, getting dynamic loads right is key for sizing motors and keeping your structure honest.
What is Coriolis Force on Rotating Links?
If a mass moves in or out along a spinning link, it gets hit with a force sideways to that movement—the Coriolis force. It's stronger the faster you move in/out or spin. Along with this, there's always a centripetal force pulling toward the center of rotation.
Simple Explanation
If you’re on a spinning merry-go-round and roll a ball out from the center, it curves off to the side—that's Coriolis force in action. On a rotating arm, anything moving along the length gets pushed sideways, and your motors or frame need to handle that force.
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Rotating Link System Diagram
Coriolis Force Calculator
This calculator is intended for education, concept evaluation, and preliminary design. Results are based on the equations and assumptions described on this page, but cannot account for every real-world load case, tolerance, material property, environmental condition, installation detail, safety factor, code, or regulatory requirement. Verify all inputs, assumptions, units, and results independently before selecting components or using the result in a real application. Safety-critical, structural, medical, lifting, transportation, or regulated applications must be reviewed by a qualified engineer.
📹 Video Walkthrough — How to Use This Calculator
Coriolis Force interactive visualizer
Watch how Coriolis and centripetal forces change as a mass moves radially along a rotating link. Adjust the parameters to see real-time force calculations for robotic arms and rotating machinery design.
CORIOLIS FORCE
10.0 N
CENTRIPETAL FORCE
20.0 N
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How to Use This Calculator
- Pick your units—metric (kg, m, m/s) or imperial (lbm, ft, ft/s).
- Fill in the mass, how fast it moves along the link (radial velocity), the angular velocity in rad/s, and the radius from your axis.
- Make sure your angular velocity is in rad/s, not RPM—take RPM and multiply by π/30 if needed.
- Hit Calculate.
Simple Example
A 5 kg mass moves radially at 0.5 m/s along a link rotating at 2 rad/s, positioned 1 m from the rotation axis.
- Coriolis Force = 2 × 5 × 0.5 × 2 = 10 N
- Centripetal Force = 5 × 2² × 1 = 20 N
Mathematical Equations
Coriolis Force
Use the formula below to calculate Coriolis force.
Where:
- FCoriolis = Coriolis force magnitude (N or lbf)
- m = Mass of the moving object (kg or lbm)
- ω = Angular velocity of the rotating frame (rad/s)
- vr = Radial velocity relative to the rotating frame (m/s or ft/s)
Centripetal Force
Use the formula below to calculate centripetal force.
Where:
- Fcentripetal = Centripetal force magnitude (N or lbf)
- r = Distance from rotation axis (m or ft)
Vector Relationships
The Coriolis force vector is perpendicular to both the angular velocity vector and the radial velocity vector, following the right-hand rule. In a rotating coordinate system:
Technical Analysis and Applications
Understanding Coriolis and Centripetal Forces
If you're looking at a rotating system from a rotating frame—think inside the arm itself—two main forces show up: Coriolis force and centripetal force. These aren't fake; they're essential for understanding loads in robotics and rotating machinery.
The Coriolis force only shows up when a mass moves in or out along the radius. It always acts perpendicular to that radial movement and the rotation axis, and it scales with both the speed of that in/out movement and how fast the system spins.
The centripetal force is what keeps the mass from flying off at a tangent; it’s always there as long as something is moving in a circle, whether or not it's moving along the link.
Engineering Applications
Robotic Arm Design
For multi-axis arms, Coriolis forces show up if the arm extends or retracts while turning. These can cause joint coupling and make path control tricky, so you need to factor them in when sizing motors or designing your control logic.
Rotating Machinery
Pumps, turbines, and similar machines deal with Coriolis and centripetal forces acting on both the parts and the fluids inside. They matter for impeller stress, bearing selection, and vibration. Secondary flows from Coriolis effects aren't always big, but they change efficiency and wear.
Precision Positioning Systems
High-speed CNCs or rotating tables need to handle these side forces, or they’ll see errors in position or chatter. That’s why the calculator helps when you want to estimate effects before you pick hardware or program compensation.
Worked Example: Robotic Arm Analysis
Suppose you have a 2 kg load, 1.5 meters from center, arm spinning at 0.5 rad/s, extending at 0.3 m/s.
Given Parameters:
- Mass (m) = 2 kg
- Radius (r) = 1.5 m
- Angular velocity (ω) = 0.5 rad/s
- Radial velocity (vr) = 0.3 m/s
Calculations:
Coriolis Force:
FCoriolis = 2 × m × vr × ω
FCoriolis = 2 × 2 kg × 0.3 m/s × 0.5 rad/s = 0.6 N
Centripetal Force:
Fcentripetal = m × ω² × r
Fcentripetal = 2 kg × (0.5 rad/s)² × 1.5 m = 0.75 N
Here, 0.6 N of Coriolis force acts sideways (tangential to the radial extension), putting a dynamic load on your drive motor. The 0.75 N centripetal force always loads the arm bearings inward.
Design Considerations
Control System Design
If you want good trajectory tracking, model these forces and feedforward-compensate for them in your servo drives. Modern controls do this by calculating Coriolis torques based on your velocity commands.
Structural Analysis
Both forces matter for sizing bearings, doing fatigue checks, and foundation design. In multi-axis machines, these time-varying loads can excite vibration modes—watch for resonance if speeds match natural frequencies.
Motor Sizing
Motors in rotating or extending/rotating systems get hit with extra torque from Coriolis forces. You usually need a higher continuous torque rating than basic calculations suggest, and the more radial motion you introduce during rotation, the more margin you’ll want.
Advanced Considerations
Multi-Link Systems
In linked multi-axis arms, Coriolis terms can couple different joint motions. The more links move together, the messier the math gets. Model these systems carefully if precision matters.
High-Speed Applications
At high RPM, Coriolis effects can swamp everything else. Fast tool changes on spinning systems or quick-moving end effectors make these forces a limiting factor for accuracy and speed.
Vibration Analysis
These side forces can create gyroscopic or cross-axis effects. Sometimes, they’ll stabilize a system, sometimes not—either way, include them in vibration checks when you're chasing down odd dynamic problems.
If you’re building or analyzing anything with rotating and moving links, include these effects in your design stage for a more reliable and realistic system outcome.
Frequently Asked Questions
What is the difference between Coriolis and centripetal forces?
When are Coriolis forces significant in engineering applications?
How do I account for Coriolis forces in motor sizing?
Can Coriolis forces cause vibration problems?
What units should I use in the Coriolis force calculator?
How do Coriolis forces affect linear actuator selection?
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About the Author
Robbie Dickson
Chief Engineer & Founder, FIRGELLI Automations
Robbie Dickson brings over two decades of engineering expertise to FIRGELLI Automations. With a distinguished career at Rolls-Royce, BMW, and Ford, he has deep expertise in mechanical systems, actuator technology, and precision engineering.
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