8. Centripetal Forces & Gravitation

a. An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle θ. Find an expression for the angular velocity ω.

Two wires are tied to the 2.0 kg sphere shown in FIGUREP8.45. The sphere revolves in a horizontal circle at constant speed. a. For what speed is the tension the same in both wires?

A 2.0 kg pendulum bob swings on a 2.0-m-long string. The bob's speed is 1.5 m/s when the string makes a 15° angle with vertical and the bob is moving toward the bottom of the arc. At this instant, what are the magnitudes of (c) the tension in the string?

2.0 kg ball swings in a vertical circle on the end of an 80-cm-long string. The tension in the string is 20 N when its angle from the highest point on the circle is θ = 30°. a. What is the ball's speed when θ = 30°?

The 10 mg bead in FIGURE CP8.69 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity ω. If ω is less than some critical value ω꜀, the bead sits at the bottom of the spinning loop. When ω > ω꜀, the bead moves out to some angle θ. a. What is ω꜀ in rpm for the loop shown in the figure?