Problem 9.60 Part A You are designing a rotating metal flywheel that will be use

Question

Problem 9.60 Part A You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 31.0 cm Starting from rest at t 0, the flywheel rotates with constant angular acceleration 3.00 rad/s2 about an axis perpendicular to the flywheel at its center If the flywheel has a density (mass per unit volume) of 8600 kg/m3, what thickness must it have to store 800 J of kinetic energy at t 8.00 s? Express your answer to three significant figures and include the appropriate units. h-Value Units Submit My Answers Give Up

Explanation / Answer

angular velocity at 8 sec

= t
= 3.00(8.00)
= 24.0 rad/s

Moment of inertia for a uniform disc
I = ½mr²
Kinetic energy of a rotating mass
KEr = ½I²
KEr = ½(½mr²)²
KEr = ¼mr²²
m = 4(KEr) /r²²
volume of a disc if h = height of cylinder
V = r²h

mass of a disc
m = V
m = r²h

r²h = 4(KEr) / r²²
h = 4(KEr) / r²

h = 4(800) / 0.31(24²)(8600)
h = 0.02227 m
h = 2.23 cm


I hope this helped.

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