Flywheels are large, massive wheels used to store energy. They can be spun up sl

Question

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.8 m diameter and a mass of 270 kg. Its maximum angular velocity is 1200 rpm Part A A motor spins up the flywheel with a constant torque of 53 N-m. How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units Value Units Submit Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units LA E- Value Units Submit Request Answer Part C

Explanation / Answer

Given,

d = 1.8 m => r = 0.9 m ; m = 270 kg ; w = 1200 rpm = 125.66rad/s

A)T = 53 Nm

We know that

T = I alpha => alpha = T/I

I = 1/2 M r^2 = 1/2 x 270 x 0.9^2 = 109.35

alpha = 53/109.35 = 0.485 rad/s^2

alpha = w/t

t = w/alpha = 125.66/0.485 = 259.1 s

Hence, t = 259.1 s (= 4.32 min)

b)KE = 1/2 I w^2

E = 0.5 x 109.35 x 125.66^2 = 8.63 x 10^5 J

Hence, E = 8.63 x 10^5 J

c)P = E/t

E = E/2 = 8.63 x 10^5/2 = 4.32 x 10^5

P = 4.32 x 10^5/2.5 = 1.88 x 10^5 W

Hence, P = 1.88 x 10^5 W = 188 kW

d)w = sqrt (E/I) = sqrt (8.63 x 10^5/109.35) = 88.84 rad/s

alpha = w/t = 88.84/2.3 = 38.63 rad/s^2

T = I alpha

T = 109.35 x 38.63 = 4224.2 Nm

Hence, T = 4224.2 Nm

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