Question

Consider an object moving with a velocity \( \vec{v} \) in a frame which rotates with a constant angular velocity \( \vec{\omega} \). The Coriolis force experienced by the object is

• A. along \( \vec{v} \)
• B. along \( \vec{\omega} \)
• C. perpendicular to both \( \vec{v} \) and \( \vec{\omega} \)
• D. always directed towards the axis of rotation

Hint:

The Coriolis force is a fictitious force in a rotating reference frame and is always perpendicular to the velocity of the object and the axis of rotation.

Answer 1

The Correct Option is C

Step 1: Understanding the Coriolis force.
The Coriolis force is a fictitious force that arises in rotating reference frames. It is given by the equation: \[ \vec{F}_C = -2m (\vec{\omega} \times \vec{v}) \] where \( m \) is the mass of the object, \( \vec{\omega} \) is the angular velocity of the rotating frame, and \( \vec{v} \) is the velocity of the object in that frame. The Coriolis force is always perpendicular to both the velocity of the object and the axis of rotation.

Step 2: Analyzing the options.
(A) along \( \vec{v} \): Incorrect. The Coriolis force is not along the velocity of the object.
(B) along \( \vec{\omega} \): Incorrect. The Coriolis force is not along the angular velocity vector; it is perpendicular to both \( \vec{v} \) and \( \vec{\omega} \).
(C) perpendicular to both \( \vec{v} \) and \( \vec{\omega} \): Correct. The Coriolis force is perpendicular to the velocity of the object and the angular velocity of the rotating frame.
(D) always directed towards the axis of rotation: Incorrect. The Coriolis force is not directed towards the axis of rotation; it is perpendicular to the plane formed by \( \vec{v} \) and \( \vec{\omega} \).

Step 3: Conclusion.
The correct answer is (C) because the Coriolis force is always perpendicular to both the velocity of the object and the angular velocity of the rotating frame.