Coriolis Force Calculator
Coriolis force is an inertial force that acts on the objects which are in motion within a rotating reference frame with respect to inertial frame. Coriolis force can be calculated using particle mass,angular velocity and velocity.
Calculator
| Coriolis Force Calculator for Rotating Reference Frame | |
|---|---|
| Particle Mass | |
| Angular Velocity | |
| Velocity | |
| Coriolis Force: | {{coriolisForceResult()}} |
How to use Coriolis Force Calculator?
Step 1 - Enter the Particle Mass
Step 2 - Enter the Angular Velocity
Step 3 - Enter the Velocity
Step 4 - Click on “Calculate” button to calculate Coriolis Force
Step 5 - Calculate Coriolis Force
Coriolis Force Equation:
F’cor = -2mω × v'
Where,
F’cor = Coriolis Force
m = Particle Mass
ω = Angular Velocity
v’ = Velocity
Frequently Asked Questions
What is the Coriolis force and how does it affect moving objects?
The Coriolis force is an apparent force experienced by objects moving in a rotating reference frame (like Earth). In an inertial frame, objects move in straight lines following Newton’s laws. In a rotating frame, these objects appear to curve due to the frame’s rotation. The force is proportional to object velocity and angular velocity of the frame. This effect is vital for understanding weather patterns, ocean currents, and ballistic missile trajectories.
How does the Coriolis effect influence atmospheric and oceanic circulation?
Earth’s rotation creates Coriolis force that deflects moving air and water masses. In the Northern Hemisphere, moving objects deflect rightward; in the Southern Hemisphere, leftward. This drives the large-scale wind patterns (trade winds, westerlies) and ocean gyres. The magnitude increases toward the poles, making Coriolis effect strongest at poles (latitude 90°) and zero at the equator. Understanding this is essential for weather prediction and climate modeling.
When is the Coriolis effect significant versus negligible?
Coriolis effect becomes significant for long-range or long-duration motion. For short distances or high velocities, direct forces dominate. The Rossby number (Ro = v/ωL) characterizes this: when Ro « 1, Coriolis dominates; Ro » 1, direct forces dominate. Ballistic trajectories, flowing rivers, and falling rain show Coriolis effects. A person walking 1 meter experiences negligible deflection, while a missile flying 1000 km must account for substantial deflection.
What is the relationship between Coriolis force and angular velocity of Earth?
Earth’s rotation provides angular velocity Ω ≈ 7.3 × 10⁻⁵ rad/s. The Coriolis force magnitude is F = 2mΩv sinφ (where φ is latitude). This small angular velocity requires velocities of at least 10+ m/s to create measurable Coriolis forces. Hurricanes, with maximum velocities 50-100 m/s, experience strong Coriolis effects essential to their structure. Slower flows in small-scale systems show negligible Coriolis effects.
How does the Coriolis force relate to terminal velocity and atmospheric motion?
Objects falling from high altitude have time to experience both Coriolis deflection and terminal velocity effects. Rain droplets reach terminal velocity of ~10 m/s, creating Coriolis deflection proportional to velocity and latitude. In ballistic problems, the object’s trajectory depends on initial velocity, and Coriolis effect causes rightward (Northern Hemisphere) deflection proportional to both velocity and time aloft.
Related Physics Calculators
- Terminal Velocity Calculator - Calculate falling speeds affected by Coriolis in long trajectories
- Electromagnetic Field Energy Density - Understand energy in rotating electromagnetic systems
Physical Basis & References
This calculator applies Rotating Reference Frame Dynamics:
$$\vec{F}_{Cor} = -2m\vec{\omega} \times \vec{v}$$
In component form (Earth’s rotation at latitude φ): $$F_{Cor} = 2m\Omega v \sin\phi$$
Key Physics Principles:
- Non-Inertial Frame - Rotating frame requires fictitious forces for Newton’s laws to apply
- Cross Product - Coriolis force perpendicular to both angular velocity and velocity
- Latitude Dependence - Force varies as sin(latitude), maximum at poles
- Rossby Number - Dimensionless parameter determining Coriolis significance
Key Assumptions:
- Reference frame rotating at constant angular velocity
- Non-relativistic velocities
- Object mass constant
- No air resistance (in basic calculation)
- Flat Earth approximation for local analysis
Typical Range of Values:
- Earth’s angular velocity: Ω = 7.3 × 10⁻⁵ rad/s
- Coriolis parameter f = 2Ω sin(φ): 0 (equator) to 1.46 × 10⁻⁴ s⁻¹ (poles)
- Velocity range: 0.1 to 100 m/s (pedestrian to aircraft)
- Object mass: 0.1 kg to 1000 kg
- Coriolis force: millionewtons to kiloNewtons (depending on parameters)
Further Reading:
- Goldstein, H. (1980). Classical Mechanics, 2nd Edition. Addison-Wesley.
- Holton, J.R. & Hakim, G.J. (2013). An Introduction to Dynamic Meteorology, 5th Edition. Academic Press.
- Coriolis Effect - NOAA and NASA educational resources