Calculation
aθ = 2 · ω · vr
A body sliding in a rotating radial slot has a transverse Coriolis acceleration in addition to its radial motion.
Relativbewegung in radial rotierender Führung · aθ = 2ω·vr
Calculate Coriolis Acceleration of a Sliding Body
A body sliding in a rotating radial slot has a transverse Coriolis acceleration in addition to its radial motion.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Transverse acceleration aθ — Signed Coriolis acceleration across the radial guide; positive is the circumferential direction for positive ω. Multiply by mass to estimate lateral guide force.
- Angular velocity ω — Angular speed of the guide about its axis from speed data or measurement; positive counter-clockwise.
- Relative radial sliding speed vr — Body speed relative to the guide along the radial slot; positive outward, negative toward the rotation axis.
Example
With ω = 2 rad/s and outward sliding speed vr = 1 m/s, aθ = 2·2·1 = 4 m/s² across the guide.
Assumptions and limits
Planar motion in a rigid radial guide about a common axis; aθ is only the Coriolis contribution to absolute acceleration. Centripetal, angular-acceleration and relative-acceleration terms require separate addition. General three-dimensional motion uses 2Ω×vrel.
Understand Coriolis acceleration in a rotating guide
A slider moves along a radial guide while the guide rotates. This calculator finds the extra lateral acceleration caused by that combined motion.
What does this quantity describe?
Coriolis acceleration is the part of absolute acceleration caused by simultaneous rotation of the guide and motion relative to it. For a radial slot, aθ = 2ωvr. Here ω is guide angular velocity, vr radial relative speed, and aθ transverse acceleration. Positive ω means counter-clockwise rotation and positive vr means outward motion; a negative result points in the opposite circumferential direction.
Formula and variables
aθ = 2 · ω · vr
Radial guide: aθ = 2ωvrGeneral vector form: aC = 2Ω×vrel
| Symbol / input | Meaning |
|---|---|
| Transverse acceleration aθ | Signed Coriolis acceleration across the radial guide; positive is the circumferential direction for positive ω. Multiply by mass to estimate lateral guide force. |
| Angular velocity ω | Angular speed of the guide about its axis from speed data or measurement; positive counter-clockwise. |
| Relative radial sliding speed vr | Body speed relative to the guide along the radial slot; positive outward, negative toward the rotation axis. |
Choose the inputs correctly
ω in rad/s comes from speed measurement or drive data: ω = 2πn/60 when n is in revolutions per minute. vr in m/s is sliding speed measured relative to the guide, for example from a displacement-time record. Either input may be positive, zero or negative to represent direction. aθ in m/s² is transverse acceleration; multiplying it by slider mass gives an estimate of lateral contact force.
How to use the calculator
Define positive rotation and radial directions. Enter angular velocity and relative sliding speed at the same instant. Read output sign using those conventions, and add the remaining motion terms separately when finding total absolute acceleration.
Worked example
A guide rotates counter-clockwise at ω = 2 rad/s. A slider moves outward at vr = 1 m/s: aθ = 2·2·1 = 4 m/s² in the positive circumferential direction. With vr = −1 m/s the result is −4 m/s².
Understand the result and units
No guide rotation or no relative sliding gives zero Coriolis acceleration. Doubling ω or vr doubles aθ. The acceleration is perpendicular to radial sliding speed.
The internal units are rad/s for ω, m/s for vr and m/s² for aθ. One revolution per minute equals 2π/60 rad/s; the existing SI registry handles unit conversion.
Typical applications
Early estimates of lateral slider loads in rotating guides, crank mechanisms and rotating test rigs.
Assumptions, limits and common mistakes
The relation assumes planar motion in a rigid, exactly radial guide and returns only the Coriolis term. Centripetal acceleration, angular acceleration of the guide and relative acceleration along the guide are excluded. Inclined or spatial motion needs the vector form 2Ω×vrel.
Common mistake: Do not enter absolute body speed as vr: vr is speed relative to the rotating guide alone. Do not confuse the result with centripetal acceleration ω²r, which depends on radius rather than sliding speed.
Frequently asked questions
What is “Coriolis acceleration in a rotating guide” used for?
Early estimates of lateral slider loads in rotating guides, crank mechanisms and rotating test rigs.
Where do the input values come from?
ω in rad/s comes from speed measurement or drive data: ω = 2πn/60 when n is in revolutions per minute. vr in m/s is sliding speed measured relative to the guide, for example from a displacement-time record. Either input may be positive, zero or negative to represent direction. aθ in m/s² is transverse acceleration; multiplying it by slider mass gives an estimate of lateral contact force.
What does the result not cover?
The relation assumes planar motion in a rigid, exactly radial guide and returns only the Coriolis term. Centripetal acceleration, angular acceleration of the guide and relative acceleration along the guide are excluded. Inclined or spatial motion needs the vector form 2Ω×vrel.