Verify Coriolis Acceleration Derivation on Merry Go Round

[somebodyelse5]

I have a derivation for the coriolis acceleration on a "merry go round" that my instructor gave in class, i was wondering if someone could tell me if this is correct or offer the correct final equation.
Additional information: this is from the rotating point of view on the merry go round.

[$$\omega$$ V$$_{}o$$cos($$\theta$$-$$\omega$$t)+$$\omega$$^2V$$_{}o$$tsin($$\theta-\omega$$t)]j-2[$$\omega$$V$$_{}o$$sin($$\theta$$-$$\omega$$t)-$$\omega$$^2V$$_{}o$$cos($$\theta$$-$$\omega$$t)]j

Note: this is not HW, just something i need to study for my exam and I am concerned it is incorrect.
V$$_{}o$$ is Initial velocity

Please forgive the poor formatting of that equation, i did my best to make it clear. For some reason, some of the omegas are off set up, and shouldn't be, could figure out why.

 

[jfy4]

This is what you wrote I think,

$$[\omega v_0\cos(\theta-\omega t)+\omega^2v_0t\sin(\theta-\omega t)]\mathbf{j}-2[\omega v_0\sin(\theta-\omega t)-\omega^2 v_0\cos(\theta-\omega t)]\mathbf{j}$$

You can just use the tex environment from now on instead of switching between them. Well the way it's written it can't be right since the last term (the one with cosine) doesn't have the units of acceleration. I imagine there should be a $t$ multiplied at the end there.

Did you mis-transcribe it?

 

[Matterwave]

The coriolis force produces acceleration:

$$\bold{a_c}=-2(\bold{\omega} \times \bold{v})$$

So, without knowing how exactly you defined your variables, and the exact set up of your problem, I'm not entirely sure I can help you all that much.

 

[somebodyelse5]

appreciate the responses guys. In my frantic searches and calls to fellow students it turns out i simply "forgot" a 2 in front of the first term, and mixed up the unit vector for the second term.

If you guys are at all interested, I can post the correct equation tomorrow? got to keep studying now!

 

[RedX]

You are missing a time variable in the second centrifugal acceleration term. You need a v*t to equal radius for someone walking radially. The 2 should only be part of the Coriolis acceleration and not the centrifugal acceleration. Your second unit vector j should be an i. Other than that you're fine. Also I'm assuming that a positive v means the person is walking radially outward, and a negative v means they are walking radially inward.

Have you tried solving for the trajectory and not just the acceleration?