Question

Problem#3 (10 points): A flywheel with a mass moment of inertia is 0.72 Kg m2 starts from rest and accelerated at the rate of 3.4 rad/s2 for 40 s. a) Determine the net torque used for the acceleration of the flywheel. b) Determine the angular velocity reached after 15 s and 35 s. c) Determine the acceleration and compare with given acceleration. Then retardation was applied to this flywheel with a rate of 3.8 rad/s2 to decrease the angular velocity to 29 rad/s d) Determine the net torque used for the retardation of the flywheel e) Determine the time taken to reduce the velocity Determine the total angular displacement of the flywheel. g) Determine the needed torque to stop the flywheel. h) Determine the needed torque to stop the flywheel if it's mass multiplied by three. What is the needed the modification that we have to consider in the design (mass of the flywheel) if we want to decrease the requested torque to stop the flywheel. D) Determine the total angular displacement from the start until the stop of the flywheel. f) 1)

Answer 1

Calculate the net torque used for the acceleration of the flywheel. Twee = la =(0.72)(3.4) = 2.448 N-m Calculate the angular velocity reached after 15 s and 35 s. m = 0, +at=0+(3.4)(15) = 51 rad/s m = 0, +at = 0+(3.4)(35) =119 rad/s Calculate the net torque used for the retardation of the flywheel. Toet = Ia =(0.72)(3.8) = 2.736 N-m Calculate the angular velocity reached after 40 s during acceleration. m = 0, +at=0+(3.4)(40) = 136 rad/s Calculate the time taken to reduce the velocity during deceleration. m), = 0 + at 136-29 29=136+(-3.8) = 28.16 sec 3.8 t= Calculate the total angular displacement of the flywheel.

Δθ = Δθ + Δθ, -o-gar)-(ar -ξαν) -o-(34) 140 )-(136)/28.16) - (38) 28 16 ) =5043.09 rad