Glossary

6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force

3 min read•june 18, 2024

arise in , like accelerating cars or rotating platforms. These apparent forces, such as the , are necessary to accurately describe motion in these frames, even though they don't result from physical interactions between objects.

The Coriolis force, observed on Earth's rotating surface, deflects moving objects perpendicular to their motion. It impacts weather patterns, projectile trajectories, and ocean currents. Understanding these effects is crucial for navigation, meteorology, and long-range ballistics.

Fictitious Forces and Non-inertial Frames

Inertial vs non-inertial frames

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  • of reference
    • Frames where of motion apply without modification
    • No net force acts on the frame itself
    • Examples include stationary frames (lab bench) and frames moving at constant velocity (train traveling at constant speed)
  • of reference
    • Frames accelerating or rotating relative to an inertial frame
    • Newton's laws require modification with fictitious forces to accurately describe motion
    • Examples include accelerating vehicles (car speeding up), rotating platforms (merry-go-round), and Earth's surface (rotating about its axis)
  • Key differences in motion analysis
    • In inertial frames, observed accelerations result from real forces like gravity or friction
    • In non-inertial frames, observed accelerations can result from a combination of real forces and fictitious forces arising from the frame's acceleration
    • Fictitious forces are apparent forces that appear due to the reference frame's acceleration, not interactions between objects

Origin of Coriolis force

  • Coriolis force arises in rotating reference frames
    • Caused by the rotation of the reference frame itself, not interactions between objects
    • Appears to deflect moving objects perpendicular to their direction of motion and the rotation axis
  • Coriolis force on Earth's surface
    • Earth rotates from west to east about its north-south axis
    • Coriolis force deflects moving objects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere
    • Magnitude of Coriolis force depends on the object's velocity, latitude, and Earth's rotation rate (7.29×10−57.29 \times 10^{-5} rad/s)
  • Coriolis force equation: Fc=−2mω⃗×v⃗F_c = -2m\vec{\omega} \times \vec{v}
    • FcF_c: Coriolis force vector
    • mm: mass of the moving object
    • ω⃗\vec{\omega}: vector of the (points along rotation axis)
    • v⃗\vec{v}: velocity vector of the object relative to the rotating frame
    • ×\times: cross product operation

Effects of Coriolis force

  • Effects on weather patterns
    • Coriolis force influences global wind patterns
      1. near the equator deflect towards the west
      2. at mid-latitudes deflect towards the east
    • Coriolis force affects cyclone and hurricane formation and rotation
      • is counterclockwise in the Northern Hemisphere (Hurricane Katrina) and clockwise in the Southern Hemisphere (Cyclone Yasi)
  • Effects on projectile motion
    • Coriolis force causes apparent deflection of projectiles
      • Deflection to the right in the Northern Hemisphere and to the left in the Southern Hemisphere
      • Deflection magnitude depends on projectile velocity, latitude, and flight time
    • Long-range projectiles like missiles and artillery shells must account for Coriolis force for accurate targeting
  • Other effects
    • Coriolis force influences ocean currents (Gulf Stream) and tidal patterns
    • Affects the motion of airplanes and ships navigating long distances (great circle routes)
    • Impacts in large-scale atmospheric and oceanic circulation patterns

Demonstrating and Measuring Coriolis Effects

  • : A simple yet powerful demonstration of Earth's rotation and Coriolis effect
  • : The key concept underlying the perception of Coriolis force in rotating frames
  • : The tendency of objects to resist changes in motion, which leads to apparent deflection in rotating frames

Key Terms to Review (25)

Angular velocity: Angular velocity is the rate of change of the rotation angle with respect to time. It is usually measured in radians per second (rad/s).
Angular Velocity: Angular velocity is a measure of the rate of change of the angular position of an object rotating around a fixed axis or point. It describes the speed of rotational motion and is a vector quantity, indicating both the magnitude and direction of the rotation.
Apparent Force: An apparent force is a fictitious force that arises in a non-inertial reference frame, such as a rotating or accelerating frame of reference. These forces appear to act on objects within the frame, even though they are not real physical forces, but rather a result of the frame's motion relative to an inertial frame.
Centrifugal force: Centrifugal force is a fictitious force that appears to act on an object moving in a circular path when viewed from a rotating reference frame. It acts outwardly away from the center of rotation.
Centrifugal Force: Centrifugal force is a fictitious force that appears to act on an object moving in a circular path, pushing the object outward away from the center of the circle. This force is not a real physical force, but rather a result of the object's inertia and the circular motion it is experiencing.
Coriolis Force: The Coriolis force is a fictitious force that appears to act on objects moving within a non-inertial reference frame, such as the Earth's surface. It is responsible for the deflection of moving objects, including air currents and ocean currents, due to the Earth's rotation.
Coriolis parameter: The Coriolis parameter is a value that represents the Coriolis effect, which is a fictitious force that arises in a non-inertial reference frame, such as the rotating Earth. It is a crucial factor in understanding the motion of objects, including air masses and ocean currents, on a global scale.
Cyclonic rotation: Cyclonic rotation refers to the counterclockwise movement of air in the Northern Hemisphere and the clockwise movement in the Southern Hemisphere around a low-pressure area. This phenomenon is closely linked to the Coriolis force, which arises from the Earth's rotation and influences wind patterns and weather systems, leading to the formation of cyclones and other atmospheric phenomena.
Euler Force: The Euler force, also known as the Euler acceleration, is a fictitious force that arises in non-inertial reference frames, such as rotating or accelerating frames of reference. It is a consequence of the fact that the laws of motion in these frames do not follow the same form as in an inertial frame, requiring the introduction of additional forces to account for the observed motion.
Fictitious force: A fictitious force, also known as a pseudo force, is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference. It arises because the non-inertial frame is accelerating or rotating relative to an inertial frame.
Fictitious Forces: Fictitious forces, also known as pseudo-forces, are apparent forces that arise in a non-inertial reference frame, such as a rotating or accelerating frame of reference. These forces are not real forces in the classical sense, but rather are mathematical constructs that account for the effects of the non-inertial motion on the observed motion of objects within that frame of reference.
Foucault Pendulum: A Foucault pendulum is a device that demonstrates the rotation of the Earth. It consists of a heavy weight suspended from a long wire or cable, and its swinging plane gradually changes direction over time, providing visual evidence of the Earth's rotation.
Gaspard-Gustave Coriolis: Gaspard-Gustave Coriolis was a French mathematician and engineer who made significant contributions to the understanding of rotational mechanics, particularly the phenomenon known as the Coriolis force. His work has become an integral part of the study of non-inertial frames and fictitious forces.
Geostrophic Flow: Geostrophic flow is a type of fluid flow in which the Coriolis force and the pressure gradient force are in balance, resulting in a flow that is parallel to the isobars (lines of constant pressure). This flow pattern is commonly observed in the atmosphere and the oceans, where the Coriolis effect plays a significant role in the dynamics of large-scale motions.
Inertia: Inertia is the resistance of an object to any change in its state of motion. It is directly proportional to the mass of the object.
Inertia: Inertia is the tendency of an object to resist changes in its state of motion. It is a fundamental property of matter that describes an object's resistance to changes in its velocity or direction of motion.
Inertial Frames: An inertial frame of reference is a coordinate system that is not accelerating or rotating. In an inertial frame, the laws of physics, such as Newton's laws of motion, apply without the need to account for any fictitious forces.
Newton's Laws: Newton's laws of motion are three fundamental principles that describe the relationship between an object and the forces acting upon it, governing the motion of physical bodies. These laws form the foundation of classical mechanics and are essential in understanding the behavior of objects in various contexts, including falling objects, problem-solving strategies, further applications of motion, and the Coriolis force in non-inertial frames.
Non-inertial frame of reference: A non-inertial frame of reference is a frame of reference that is accelerating, either linearly or rotationally. In such frames, fictitious forces like the Coriolis force and centrifugal force appear to act on objects.
Non-inertial Frames: A non-inertial frame of reference is a frame of reference that is accelerating or rotating relative to an inertial frame. In such frames, fictitious forces, such as the Coriolis force, appear to act on objects, even though no external force is actually present.
Non-inertial Reference Frames: A non-inertial reference frame is a frame of reference that is accelerating or rotating relative to an inertial reference frame. In such a frame, additional fictitious forces, like the Coriolis force, appear to act on objects, even though no real forces are present.
Relative Motion: Relative motion refers to the motion of an object as observed from a particular frame of reference or point of view. It describes the relationship between the movement of an object and the movement of the observer or reference frame.
Rotating Frame: A rotating frame of reference is a coordinate system that rotates with respect to an inertial (non-accelerating) frame. It is a type of non-inertial frame, where the laws of motion are more complex due to the presence of fictitious forces, such as the Coriolis force.
Trade Winds: Trade winds are the prevailing winds that blow from the subtropical high-pressure belts toward the equator in both the Northern and Southern Hemispheres. These winds play a crucial role in the context of Fictitious Forces and Non-inertial Frames, specifically the Coriolis Force, which governs the direction and behavior of these winds.
Westerlies: The westerlies are the prevailing winds in the middle latitudes between 30 and 60 degrees latitude, blowing from the west to the east. These winds are a critical component of the global atmospheric circulation patterns and play a significant role in the Coriolis effect and the formation of non-inertial reference frames.
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