9.40 .. You need to design an industrial turntable that is 60.0 cm in diameter and has a kinetic energy of 0.250 J when turning at 45.0 rpm (rev/min). (a) What must be the moment of inertia of the turntable about the rotation axis? (b) If your workshop makes this turntable in the shape of a uniform solid disk, what must be its mass?

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Casey DurganLv2

12 Dec 2017

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As a gasoline engine operates, a flywheel turning with the crankshaft stores energy after each fuel explosion, providing the energy required to compress the next charge of fuel and air. For the engine of a certain lawn tractor, suppose a flywheel must be no more than 18.0 cm in diameter. Its thickness, measured along its axis of rotation, must be no larger than 8.00 cm. The flywheel must release energy 60.0 J when its angular speed drops from 800 rev/min to 600 rev/min. Design a sturdy steel (density 7.85 × 10³ kg/m³) flywheel to meet these requirements with the smallest mass you can reasonably attain. Specify the shape and mass of the flywheel.

ultramarinerhinoceros942

As a gasoline engine operates, a flywheel turning with the crankshaft stores energy after each fuel explosion, providing the energy required to compress the next charge of fuel and air. For the engine of a certain lawn tractor, suppose a flywheel must be no more than 18.0 cm in diameter. Its thickness, measured along its axis of rotation, must be no larger than 8.00 cm. The flywheel must release energy 60.0 J when its angular speed drops from 800 rev/min to 600 rev/min. Design a sturdy steel (density 7.85 x 10³ kg/m³) flywheel to meet these requirements with the smallest mass you can reasonably attain. Specify the shape and mass of the flywheel.

greytrout41

The moment of inertia of a uniform-density disk rotating about anaxle through its center can be shown to be (1/2)MR2. This result isobtained by using integral calculus to add up the contributions ofall the atoms in the disk (see Problem 9.3). The factor of 1/2reflects the fact that some of the atoms are near the center andsome are far from the center; the factor of 1/2 is an average ofthe square distances. A uniform-density disk whose mass is 15 kgand radius is 0.15 m makes one complete rotation every 0.3 s.

(a) What is the moment of inertia of this disk?
I = kgÂ·m2
(b) What is its rotational kinetic energy?
Krot = J
(c) What is the magnitude of its rotational angular momentum?
Lrot = kgÂ·m2/s

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