Exercise 9.45 Energy is to be stored in a flywheel in the shape of a uniform sol

Question

Exercise 9.45

Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of R = 1.16 mand a mass of 75.0 kg . To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3450 m/s2 .

Part A

What is the maximum kinetic energy that can be stored in the flywheel?

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Exercise 9.45

Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of R = 1.16 mand a mass of 75.0 kg . To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3450 m/s2 .

Part A

What is the maximum kinetic energy that can be stored in the flywheel?

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Explanation / Answer

here,

mass , m = 75 kg

radius , r = 1.16 m

maximum allowed radial acceleration of a point on its rim = 3460 m/s^2

3460 = v^2 /r

3460= v^2 / 1.16

v = 63.63m/s

let w be the angular velocity

and we know v = r * w

63.63 = 1.16 * w

w = 54.85 rad /s

moment of inertia of flywheel, I = m * r^2/2

I = 75 * 1.16^2 / 2

I = 50.46 Kg.m^2

maximum kinetic energy that can be stored in the flywheel ,KE = rotational kinetic energy

KE = 0.5 * I * w^2

KE = 0.5 * 50.46 * 54.85^2

KE = 75905.02 J

the maximum kinetic energy that can be stored in the flywheel is 75905.02 J

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