Question

20) The 210-meter-diameter Ain Dubai Ferris Wheel is set to be completed this year. If one trip around takes a leisurely 20 minutes, what is the angular acceleration in m/s2? a. b. In order to feel weightless at the top, a centripetal acceleration equal to g is required. How long would a revolution take in this case?

Answer 1

A ).the time taken for one trip is 20 minutes or 1200s assuming the wheel started from rest initial angular velocity is zero and time taken to cover the 360degree angular distance is 1200s we have $\theta =\frac{1}{2}\alpha t^2$

where theta is angular distance and alpha is angular acceleration and t is time from this angular acceleration= 2*distance/t^2= 8.726*$10^{-6}$

the same in m/s^2 will be 8.726*10^-6 * 105 =$9.16 * 10^{-4} m/s^{2}$

B )in order to feel weightlessness at the top most point the centrifugal Acceleration should be g(9.8 m/s2)the formula for centrifugal Acceleration is$\frac{v^{2}}{r}$ = 9.8 ==>$v^2$ =r*9.8==>v=$sqrt(r * 9.8)$= 32.078m/s

one revolution means the Time taken to cover the perimeter of circle (2$\pi$r)= 2*3.14*105=659.4m

==> time taken = distance/velocity=659.4/32.078= 20.55s