Minimun angular velocity for a wheel to maintain contact with a plate

  • Thread starter samee
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I guess point A is the origin of my stationary axis, with Y going up along AB, then X going along AC. My moving axes would be at the center of the moving disk at point C.

So, the w of the small disk is induced by the Ω of the main shaft along AB. If the radius of the small wheel is r, then w=-R/rΩi+Ωj

because; V(D)=RΩ from the main shaft. V(D)=rw2 from the disk, but V(D)=V(D), so rw2=RΩ and w2=RΩ/r

okay!

This is all well and good, but shouldn't the small wheel touch the plate no matter what it's angular velocity? The answers are (a) Ω=√(g/a), and (b) Ω=√(2g/a) so I guess there is an answer that I'm just not understanding...
 

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