An electric motor can accelerate a Ferris wheel of momentof inertia I = 20000kg·

Question

An electric motor can accelerate a Ferris wheel of momentof inertia I = 20000kg·m2 from rest to 9.7 rev/min in 12.0 s. Whenthe motor is turned off, friction causes the wheel to slow downfrom 9.7 to 7.7 rev/min in 10.0 s. (a) Determine the torque generated by the motor to bring thewheel to 9.7 rev/min. (b) Determine the power that would be needed to maintain thisrotational speed.
An electric motor can accelerate a Ferris wheel of momentof inertia I = 20000kg·m2 from rest to 9.7 rev/min in 12.0 s. Whenthe motor is turned off, friction causes the wheel to slow downfrom 9.7 to 7.7 rev/min in 10.0 s. (a) Determine the torque generated by the motor to bring thewheel to 9.7 rev/min. (b) Determine the power that would be needed to maintain thisrotational speed.
(a) Determine the torque generated by the motor to bring thewheel to 9.7 rev/min. (b) Determine the power that would be needed to maintain thisrotational speed.

Explanation / Answer

   Given         moment ofinertia I = 20000 kg / m2          angularspeed   = 9.7 rev / min                        1 rev / min = 0.1047 rad / sec                         so   = 9.7 x 0.1047 rad / sec                                    = 1.01559 rad / sec              torque   = I      where =   / t                    = 1.01559/ 12                     = 0.0846          = 20000x 0.0846                = 1692         power   P =                         = 1.692 x 1.01559                         = 1718 W

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