- #1
mrdoe
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Homework Statement
A small bead with a mass of 100 g slides without friction along a rotating semicircular steel wire, where the semicircle has radius 10cm. The steel wire rotates about a vertical axis at a rate of 2 revolutions per second. Find the positions at which the bead will be motionless relative to the rotating steel wire, if the bead is in the lower half of the semicircle. Gravity points in the direction of the steel wire's axis. All surfaces are frictionless.
2. The attempt at a solution
We have the centripetal force which is in the horizontal direction to the left, which is $\dfrac{mv^2}{r} = 16000\pi^2$. We also have the velocity in the forwards direction, which is not accelerating (?) so there's no force, right? We also have the combined force of gravity and the normal force, which is $100g\sin\theta$, where $\theta$ is the counterclockwise angle from the down direction. But I don't see any force having any component pointing upwards! How does the bead stay motionless!?