Rotational Kinematics-Bead Constrained in a Hoop Rotating

AI Thread Summary
The discussion focuses on solving a problem involving a bead constrained in a rotating hoop. The participant initially uses the equation a = w^2 * r to relate acceleration and angular velocity but questions the dimensional consistency of their approach. After feedback highlighting a mistake in equating force and acceleration, they correct their equation by incorporating mass, leading to the revised formula for theta as arccos(-g/(Rw^2)). The conversation emphasizes the importance of dimensional analysis in physics problems. The final answer provided is now deemed correct based on the adjustments made.
Darkalyan
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Homework Statement


http://docs.google.com/Doc?id=d277r7r_58d3chgqfj


Homework Equations


a=w^2*r


The Attempt at a Solution



a=w^2*r
w^2*r*cos(theta)=-mg

theta=arcos(-mg/(Rw^2))

I'm pretty sure that's right, because the vertical component of the acceleration has to equal the vertical component due to gravity. However, I wasn't sure if acceleration was simply w^2*R or if I had to do something more complicated to find it. Is my reasoning/answer correct?
 
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That's pretty close. You can see it's not quite right, though, because your second equation in your attempt at a solution part is dimensionally inconsistant. You have a force equal to an acceleration.
 
oooh. didn't catch that. thank you. so then i just add a m to the left side of the equation, which makes the m's cancel out, and the final answer is theta=arcos(-g/(Rw^2)) Is that right now?
 

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