1. The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle (r = 11.6 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.760, and the angle θ in the drawing is 36.8°. How much time is required for your suitcase to go around once?
2. A motorcycle is traveling up one side of a hill and down the other side. The crest of the hill is a circular arc with a radius of 32.0 m. Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road.
3. In an automatic clothes dryer, a hollow cylinder moves the clothes on a vertical circle (radius r = 0.39 m), as the drawing shows. The appliance is designed so that the clothes tumble gently as they dry. This means that when a piece of clothing reaches an angle of θ above the horizontal, it loses contact with the wall of the cylinder and falls onto the clothes below. How many revolutions per second should the cylinder make in order that the clothes lose contact with the wall when θ = 69.0°?
4. The blade of a windshield wiper moves through an angle of 90.0° in 0.44 s. The tip of the blade moves on the arc of a circle that has a radius of 0.34 m. What is the magnitude of the centripetal acceleration of the tip of the blade?
5. Each of the space shuttle's main engines is fed liquid hydrogen by a high-pressure pump. Turbine blades inside the pump rotate at 630 rev/s. A point on one of the blades traces out a circle with a radius of 0.023 m as the blade rotates.
(a) What is the magnitude of the centripetal acceleration that the blade must sustain at this point?
(b) Express this acceleration as a multiple of g = 9.80m/s2.