# Horizontal component of the Coriolis force

• MatinSAR
MatinSAR
Homework Statement
Show that the horizontal component of the Coriolis force is independent of the direction of motion of the particle on Earth's surface.(The particle is moving on a horizontal plane.)
Relevant Equations
Newton's Laws in non-inertial reference frames.
The coriolis force that acts on the object moving on the Earth is: $$F_{cor}=2m(\vec v \times \vec \omega)$$##F_{cor}## is the Coriolis force, ##m## is the mass of the object, ## \vec{v}## is the velocity of the object in the Earth frame, and ## \vec{\omega}## is the angular velocity of the Earth.

Is it true to say that the horizontal component of this force is equal to ##2m \omega v \sin \theta## where ##\theta## is the angle between ##\vec \omega## and ##\vec v##?

MatinSAR said:
Is it true to say that the horizontal component of this force is equal to ##2m \omega v \sin \theta## where ##\theta## is the angle between ##\vec \omega## and ##\vec v##?
That is the formula for the magnitude of the Coriolis force. Not for its horizontal component.

MatinSAR
jbriggs444 said:
That is the formula for the magnitude of the Coriolis force. Not for its horizontal component.
Thank you for pointing out my mistake. I think I need to reread this chapter before trying to solve.

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