A Ferris wheel with a diameter of 35.0 m in , starts from rest and achieves...

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A Ferris wheel with a diameter of 35.0 m in , starts from restand achieves its maximum operational tangential speed of 2.20 m/sin a time of 15.0 s. a.) what is the magnitude of the wheel

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Diameter (d) of the Ferris wheel = 35.0 m
Radius (r) of the Ferris wheel = (35.0m)/2
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 17.5 m
Initial velocity (u) of the wheel = 0
Final velocity (v) of the wheel = 2.20 m/s
Time (t) taken to reach its maximum speed = 15.0 s

Then linear acceleration (a) of the wheel is
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â a = (v - u)/t
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (2.20m/s - 0)/(15.0s)
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.147 m/s^2

Then angular acceleration (a) of the wheel is
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â a = a / r

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (0.147 m/s^2) / (17.5m)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.0084 rad/s^2

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