A single bead can slide with negligible friciton on a wire that is bent into a circular loop of radius 15.0 cm. The circle is always in a vertical plane and rotates steadily about its vertical diameter with (a) a period of 0.450s. The position of the bead is described by the angle theta that the radial line, from the center of the loop to the bead, makes with the vertical. At what angle up from the bottom of the circle can the bead stay motionless relative to the turning circle? (b) Repeat the problem if the period of the circle's rotation is 0.850s.

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## Answers (1)

Trying for wow #2---

R = .15 m

ω = 2π/T = 13.963 rad/sec

A little vector diagram shows that tanθ = rω²m/mg = rω²/g

but r = Rsinθ, so tanθ = sinθ/cosθ = Rsinθω²/g from which

1/cosθ = secθ = Rω²/g = .15*13.963²/9.8 = 2.984 → θ = 70.42°

You get to do b)

Good luck..