A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of 10 m. The hoop rotates at a constant rate about a vertical diameter. Find the height of the b

Question

A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of 10 m. The hoop rotates at a constant rate about a vertical diameter. Find the height of the bead (in m) above the bottommost point if the angular velocity of rotation is 0.5 rad/ sec.

TestHub · Accepted Answer

For a nonzero angle β from the vertical, normal-force components require

$N cos β = m g, N sin β = m ω^{2} R sin β$

$cos β = \frac{g}{ω ^{2} R} = \frac{10}{( 0.5 ) ^{2} ( 10 )} = 4$

No nonzero angle can satisfy cos β = 4. The stable position is at the bottom.

$h = 0 m$

Physics - Circular Motion Question with Solution | TestHub

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