The New York Wheel is the world\'s largest Ferris wheel. It\'s 183 meters in dia

Question

The New York Wheel is the world's largest Ferris wheel. It's 183 meters in diameter and rotates once every 37.3 min.

a) find the magnitude of the average velocity at the wheels rim over a 9.00 min interval

b) find the magnitude of the average acceleration at the wheels rim over a 9.00 min interval

c) find the magnitude of the wheels instantaneous acceleration

d) Determine the ratio of the difference between the magnitude of the wheel's instantaneous acceleration and the magnitude of the average acceleration to the magnitude of the average acceleration.

Explanation / Answer

displacement covered during one complete rotation is 2*pi*(d/2) = pi*d = 3.142*183 = 574.986 m

it takes 37.3 min to cover 575 m

then in 9 mins it covers 9*575/(37.3) = 139 m

A) average velocity   = 139/(9*60) = 0.26 m/s

B) Average accelaration a = dv/dt = 0.26/(9*60) = 4.75*10^-4 m/s^2

C) instantaneous accelaration a= v^2/r = (0.26*0.26)/(183/2) = 7.4*10^-4 m/s^2

D)required ratio is (7.4-4.75)/4.75 = 0.56

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