Phys 1001 Exercise 10 You are designing an industrial flywheel, a device for sto

Question

Phys 1001 Exercise 10 You are designing an industrial flywheel, a device for storing mechanical energy in the form of rotational kinetic energy (the stored energy can be harnessed by engaging a clutch). The design requirements are that the flywheel should store 250 kJ of energy when rotating at 1500 rpm, the radius of the flywheel should be 55 cm, and it is to be made from steel with a density of 7850 kg/m3. (a) Find the required rotational inertia. (b) If the flywheel is to be constructed as a simple disk, what will its mass need to be? (c) How thick would the disk need to be?

Explanation / Answer

E = 1/2 I w^2

w= 1500 rpm = 157.1 rad/sec

250 x 10^3 = (0.5) ( I) ( 157.1^2)

I = 20.26 kg m^2

250 x 10^3 = 0.5 (1/ 2mr^2) ( w^2)

250 x 10^3 = ( 0.25 ) ( m ) (157.1^2) (0.3025)

m = 133.943 kg

mass = density x volume

133. 943 = 7850 ( pi r^2) h

133.943 = 7850 ( 3.14 ) (0.3025)h

h or thickness= 1.796 cm apprx

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