The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of $100$ m. Its name comes from its $60$ arms, each of which can function as a second hand (so that it makes one revolution every $60.0$ s). Find the speed of the passengers when the Ferris wheel is rotating at this rate.

The 'Giant Swing' at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable $5.00$ m long, and the upper end of the cable is fastened to the arm at a point $3.00$ m from the central shaft (Fig. E$5.50$). Find the time of one revolution of the swing if the cable supporting a seat makes an angle of $30.0°$ with the vertical.

The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of $100$ m. Its name comes from its $60$ arms, each of which can function as a second hand (so that it makes one revolution every $60.0$ s). What would be the time for one revolution if the passenger's apparent weight at the highest point were zero?

The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of $100$ m. Its name comes from its $60$ arms, each of which can function as a second hand (so that it makes one revolution every $60.0$ s). What then would be the passenger's apparent weight at the lowest point?

In another version of the 'Giant Swing' (see Exercise $5.50$), the seat is connected to two cables, one of which is horizontal (Fig. E$5.51$). The seat swings in a horizontal circle at a rate of $28.0$ rpm (rev/min). If the seat weighs $255$ N and an $825$-N person is sitting in it, find the tension in each cable.

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?

The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of $100$ m. Its name comes from its $60$ arms, each of which can function as a second hand (so that it makes one revolution every $60.0$ s). A passenger weighs $882$ N at the weight-guessing booth on the ground. What is his apparent weight at the highest and at the lowest point on the Ferris wheel?