What is coriolis acceleration?

Short Answer:

Coriolis acceleration is a type of acceleration that occurs when a point moves along a rotating link or body. It is produced due to the combination of linear motion of a point and the angular motion of the link on which the point lies. The direction of Coriolis acceleration is always at right angles to the path of motion and depends on the direction of rotation.

This acceleration is mainly observed in mechanisms where a slider moves on a rotating link, such as in a crank and slotted lever quick return mechanism. It plays an important role in analyzing the motion of links in mechanisms involving rotation and translation.

Detailed Explanation :

Coriolis Acceleration

Coriolis acceleration is an additional or secondary acceleration that appears in a system when a point is moving along a path on a rotating body. It arises when a body has both linear (translational) motion and rotational motion at the same time. In simple terms, it is the acceleration caused by the change in direction of the velocity of a point due to rotation of the link along which it is sliding.

In mechanical systems, Coriolis acceleration is an important concept in kinematics, as it helps to determine the actual acceleration of a moving part. When a point moves along a rotating link, its velocity direction changes continuously because the link itself is rotating. This change in the direction of velocity causes an additional acceleration component known as Coriolis acceleration.

The magnitude of Coriolis acceleration is given by:

where,

  •  = Coriolis acceleration
  •  = angular velocity of the rotating link (in rad/s)
  •  = linear velocity of the sliding point (in m/s)

The factor ‘2’ in the equation indicates that Coriolis acceleration is twice the product of angular velocity and linear velocity.

Explanation of Coriolis Acceleration

To understand Coriolis acceleration clearly, consider a simple example where a slider moves along a rotating arm. Suppose the arm OA rotates about a fixed point O with an angular velocity . A slider P moves along the arm OA with a velocity  relative to the arm.

Now, as the arm OA rotates, the direction of motion of the slider P changes continuously. Because of this rotation, an additional acceleration acts on the slider, which is known as Coriolis acceleration. This acceleration acts in a direction perpendicular to the path of motion of the slider, that is, at 90° to its velocity direction.

  • The magnitude of Coriolis acceleration depends on both the angular speed of rotation of the arm and the linear speed of the slider.
  • The direction of Coriolis acceleration is determined by the sense of rotation (clockwise or counterclockwise) and the direction of sliding.

If the rotation of the link is clockwise and the slider moves outward, the direction of Coriolis acceleration will be perpendicular and directed tangentially to the path. If the rotation is counterclockwise and the slider moves inward, the direction of Coriolis acceleration will change accordingly.

Physical Significance

Coriolis acceleration is not due to any applied force but is a kinematic effect caused by the combination of motions. It represents the apparent change in acceleration that an observer notices due to motion on a rotating frame. It is significant in mechanical linkages, rotating systems, and even in meteorological phenomena such as the movement of air currents and ocean currents on Earth due to the planet’s rotation.

In mechanisms, such as crank and slotted lever mechanisms, Whitworth quick return mechanisms, and rotating sliders, Coriolis acceleration plays an important role in analyzing the complete motion of moving parts. It affects the velocity and acceleration diagrams of mechanisms and is essential for precise motion analysis.

Direction of Coriolis Acceleration

The direction of Coriolis acceleration can be found by a simple rule:

  • Rotate the velocity vector of the sliding point through 90° in the direction of angular velocity (ω) of the rotating link.
    The resulting direction gives the line of action of Coriolis acceleration.

For example, if the arm rotates clockwise, then rotate the velocity vector of the slider 90° clockwise to find the direction of Coriolis acceleration. If the arm rotates anticlockwise, rotate the velocity vector 90° anticlockwise.

Applications in Mechanisms

Coriolis acceleration appears in mechanisms that combine rotational and translational motions, such as:

  1. Crank and slotted lever quick return mechanism – The slider moving along a rotating slotted link experiences Coriolis acceleration.
  2. Whitworth quick return mechanism – The slotted lever and slider produce Coriolis acceleration during motion.
  3. Slotted bar mechanisms – Where a sliding point moves over a rotating bar.
  4. Planetary and epicyclic gear systems – When gears rotate and move simultaneously.
  5. Engineering dynamics and Earth’s rotation studies – Coriolis effect is used to explain movement of winds and projectiles.
Conclusion:

Coriolis acceleration is the acceleration that arises when a point moves on a rotating body or link. It results from the combined effect of linear motion along the link and rotational motion of the link itself. Its magnitude is twice the product of angular velocity and linear velocity, and it always acts perpendicular to the path of motion. Understanding Coriolis acceleration is essential for analyzing complex mechanisms like quick-return mechanisms and other rotating systems where both translation and rotation occur together.