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 = 1.19 mand a mass of 71.0 kg . To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3410 m/s2 .

Part A

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

Exercise 9.45

Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of R = 1.19 mand a mass of 71.0 kg . To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3410 m/s2 .

Part A

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

Explanation / Answer

Here ,

let the maximum angular speed is w

maximum angular acceleration , a = 3410 m/s^2

as a = w^2 * r

3410 = w^2 * 1.19

w = 53.53 rad/s

Now , maximum kinetic energy stored = 0.5 * I * w^2

maximum kinetic energy stored = 0.5 * 0.5 * m * r^2 * w^2

maximum kinetic energy stored = 0.5 * 0.5 * 71 * 1.19^2 * 53.53^2

maximum kinetic energy stored = 72025.6 J

the maximum kinetic energy stored is 72025.6 J

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