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## Homework Statement

A particle has velocity v on a smooth horizontal plane. Show that the particle will move in a circle due to the rotation of the earth and find the radius of the circle. (Ignore all fictitious forces except the Coriolis force.)

## Homework Equations

Coriolis force, given by

**F**= -2m(

_{C}**ω**x

**v**)

## The Attempt at a Solution

I started off by writing out the vector ω:

**ω**=ω

_{x}+ω

_{y}+ω

_{z}

But the x component of the earth's angular velocity is zero.

The velocity of the particle is horizontal, so has no z component.

So I tried calculating the cross product of ω and v and ended up with:

F

_{C}=-2m[(-ω

_{z}v

_{y})i + (ω

_{z}v

_{x})j + (-ω

_{y}v

_{x})k]

This is where I got stuck..I'm not sure how I'm supposed to show that this causes circular motion. I'd assume I'm looking for a force perpendicular to v...

If anyone can give me any advice or let me know what I'm doing wrong I'd appreciate it!

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