A Ferris wheel rotates because a motor exerts a torque on thewheel. The radius o

Question

A Ferris wheel rotates because a motor exerts a torque on thewheel. The radius of the London Eye, a huge observation wheelon the banks of the Thames, is 67.5 m and its mass is 1.90 x10^6kg. The cruising angular speed of the wheel is 3.50 x 10^-3rad/s. a) How much work does the motor need to do to bringthe stationary wheel up to cruising speed? b) What is thetorque (assumed constant) the motor needs to provide to the wheelif it takes 20.0 seconds to reach the cruising angular speed?
(A) (a) 5.30 × 104 J (b) 1.51 × 106 Nm (B) (a)5.30 × 104 J (b) 2.64 × 106 Nm
(C) (a) 7.42 × 104 J (b) 1.51 × 106 Nm (D) (a)7.42 × 104 J (b) 3.11 × 106 Nm
(E) (a) 6.67 × 104 J (b) 1.98 × 106 Nm

Explanation / Answer

Mass of ther wheel M =  1.90 x10^6 kg
radius of the wheel R = 67.5 m Initial angular speed w = 0 rade / s The cruising angular speed of the wheel w ' = 3.50x 10^-3 rad/s We know work done W = change in rotationalK.E                                        = ( 1/ 2) I [ w ' 2 - w 2 ]                                       =  ( 1/ 2) I w ' 2 where I = Mpment of inertia of the wheel = ( 1/ 2) M R2 Substitue values weget work done W  value (b). Torque ( ) = I From the relation w ' = w + t Angular accleration = ( w ' - w ) / t where t = 20 s Substitue values weget value , fromthis    value we find torque value Substitue values weget work done W  value (b). Torque ( ) = I From the relation w ' = w + t Angular accleration = ( w ' - w ) / t where t = 20 s Substitue values weget value , fromthis    value we find torque value

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