Why must mine tailings be stored and disposed of carefully?

The crank oa rotates in the vertical plane with a constant clockwise angular velocity ω0 of 5.6 rad/s. for the position where oa is horizontal, calculate the force under the light roller b of the 10.6-kg slender bar ab.

Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.15 times a second. a tack is stuck in the tire at a distance of 0.373 m from the rotation axis. noting that for every rotation the tack travels one circumference (a) find the tack's tangential speed. (b) what is the tacks radial acceleration?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)