How Is the Period of Uniform Circular Motion Affected by Latitude?

[stunner5000pt]

COnsider a large horizontal frictionless area on the Earth at phi degrees northern latitude. Through an impulse a particle is set in motion with velocity v and then left to move freely ignore all forms of friction. Find the period in the uniformcircular motion of the particle

velocity $$v = \omega r$$
$$v_{x} = v cos \phi$$
$$v_{y} = v sin \phi$$
$$v_{z} = 0$$
not sure about the z part...

period $$T = \frac {2 \pi }{\omega sin \phi}$$
sin phi because the Y axis the one about which this motion is going about..

I am off by a factor of 2 the answer is $$T = \frac{\pi}{\omega sin \phi}$$

 

[ramollari]

What is the initial direction of the velocity vector?

 

[stunner5000pt]

The question i have typed is straight out of the textbook. I'm being rude when i say this it is the only way to say this but don't ask me questions about the question. If you care where this question came from look in JM Knudsen and PG Hjorth's Elements of Newtonian Mechanics