BackThe earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the plane's angular velocity with respect to the earth's surface? Give your answer in °/h.
A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis (Fig. 5–58) at a frequency f. If ƒ = 2.00 rev/s and r = 25.0cm, what is θ?
Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 x 106 m, and the altitude of a geosynchronous orbit is 3.58 x 107 m (≈ 22,000 miles). What are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?
FIGURE P8.54 shows two small 1.0 kg masses connected by massless but rigid 1.0-m-long rods. What is the tension in the rod that connects to the pivot if the masses rotate at 30 rpm in a horizontal circle?
A flat puck (mass M) is revolved in a circle on a frictionless air hockey table top, and is held in this orbit by a light cord which is connected to a dangling mass (mass m) through a central hole as shown in Fig. 5–51. Show that the speed of the puck is given by v = √(mgR/M).
A bug walks outward from the center of a turntable that is rotating at 65 rpm. If the coefficient of static friction between the bug and the turntable is 0.42, how far out from the center does the bug get before it starts to slip on the turntable? What happens to the bug after it moves farther out past that point?
A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis (Fig. 5–58) at a frequency f. Determine the angle θ where the bead will be in equilibrium within the hoop—that is, where it will have no tendency to move up or down along the hoop.
The position of a particle moving in the xy plane is given by , where r is in meters and t is in seconds. Show that the acceleration vector always points toward the center of the circle.
As the earth rotates, what is the speed of a physics student in Miami, Florida, at latitude 26°. Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km.
How many revolutions per minute would a 22-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?
A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis (Fig. 5–58) at a frequency f. Can the bead ride as high as the center of the circle (θ = 90°)? Explain.