8. Centripetal Forces & Gravitation

In uniform circular motion, how are the period $T$ and frequency $f$ of the motion related?

In uniform circular motion, how does the period $T$ change as the orbital radius $r$ increases, assuming the speed remains constant?

In uniform circular motion, what is the mathematical relationship between the period $T$ and the frequency $f$?

If the period of an object in uniform circular motion were doubled, what would happen to its frequency? ($f=\frac{1}{T}$)

For an alternating current with a frequency of $60\mathrm{Hz}$, what is the period of the oscillation?

In the context of uniform circular motion, about how long does it take for Earth to complete a full rotation on its axis (i.e., what is the period $T$ of Earth's rotation)?

In simple harmonic motion, what is the mathematical relationship between the frequency $f$ and the period $T$?

A wave is traveling with a frequency of $0.100 \mathrm{Hz}$. What is the period of the wave?

What is the relationship between the frequency $f$ and the period $T$ in uniform circular motion?

In uniform circular motion, how are the $f$ (frequency) and $T$ (period) of the motion related to each other?

In uniform circular motion, how are the period $T$ and frequency $f$ related to each other?

A 3kg rock spins horizontally at the end of a 2m string at 90 RPM. Calculate its centripetal acceleration.

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. How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

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. 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?

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?