Question

An electric motor can accelerate a ferris wheel of moment of inertia

Answer 1

An electric motor can accelerate a Ferris wheel of moment of inertia I = 19500 kg·m2 from rest to 9.0 rev/min in 12.0 s. When the motor is turned off, friction causes the wheel to slow down from 9.0 to 7.0 rev/min in 10.0 s. (a) Determine the torque generated by the motor to bring the wheel to 9.0 rev/min.... show more

friction acceleration  

αf = (7.0 - 9.0)rev/min * 2πrad/rev * 1min/60s / 10.0s = -0.021 rad/s²  

net acceleration  

αn = 9.0rev/min * 2πrad/rev * 1min/60s / 12.0s = 0.079 rad/s²  

(a) applied torque = moment of inertia * (net accel + friction accel)  

τ = 19500kg·m² * (0.079 + 0.021)rad/s² = 1940 N·m  

(b) Constant speed means that only the friction needs to be overcome:  

τ = 19500kg·m² * 0.021rad/s² = 408 N·m, and  

power P = τ*ω = 408N·m * (9.0rev/min * 2πrad/rev * 1min/60s) = 385 W  

seems reasonable  

Hope this helps!