8. Centripetal Forces & Gravitation

Period and Frequency in Uniform Circular Motion

Multiple Choice
A 3kg rock spins horizontally at the end of a 2m string at 90 RPM. Calculate its centripetal acceleration.
Open Question
At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. (c) How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?
Open Question
One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates 'artificial gravity' at the outside rim of the station. (a) If the diameter of the space station is 800 m, how many revolutions per minute are needed for the 'artificial gravity' acceleration to be 9.80 m/s2?
Open Question
It is proposed that future space stations create an artificial gravity by rotating. Suppose a space station is constructed as a 1000-m-diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. What rotation period will provide 'normal' gravity?
Open Question
In the Bohr model of the hydrogen atom, an electron (mass m = 9.1 x 10^-31 kg) orbits a proton at a distance of 5.3 x 10^-11 m. The proton pulls on the electron with an electric force of 8.2 x 10^-8 N. How many revolutions per second does the electron make?
Open Question
A science-fiction tale describes an artificial “planet” in the form of a band completely encircling a sun (Fig. 6–38). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth–Sun distance (to make the climate livable), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution (this planet’s year) in Earth days? <IMAGE>