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Exploring Energy ConceptsA disk-shaped flywheel, of
Chapter 2, Problem 11P(choose chapter or problem)
A disk-shaped flywheel, of uniform density \(\rho\), outer radius R, and thickness w, rotates with an angular velocity \(\omega\), in rad/s.
(a) Show that the moment of inertia, \(I=\int_{\text {vol }} \rho r^2 d V\), can be expressed as \(I=\pi \rho w R^4 / 2\) and the kinetic energy can be expressed as \(\mathrm{KE}=I \omega^2 / 2\).
(b) For a steel flywheel rotating at 3000 RPM, determine the kinetic energy, in \(\mathrm{N} \cdot \mathrm{m}\), and the mass, in kg, if \(R=0.38 \mathrm{~m}\) and \(w=0.025 \mathrm{~m}\).
(c) Determine the radius, in m, and the mass, in kg, of an aluminum flywheel having the same width, angular velocity, and kinetic energy as in part (b).
Questions & Answers
QUESTION:
A disk-shaped flywheel, of uniform density \(\rho\), outer radius R, and thickness w, rotates with an angular velocity \(\omega\), in rad/s.
(a) Show that the moment of inertia, \(I=\int_{\text {vol }} \rho r^2 d V\), can be expressed as \(I=\pi \rho w R^4 / 2\) and the kinetic energy can be expressed as \(\mathrm{KE}=I \omega^2 / 2\).
(b) For a steel flywheel rotating at 3000 RPM, determine the kinetic energy, in \(\mathrm{N} \cdot \mathrm{m}\), and the mass, in kg, if \(R=0.38 \mathrm{~m}\) and \(w=0.025 \mathrm{~m}\).
(c) Determine the radius, in m, and the mass, in kg, of an aluminum flywheel having the same width, angular velocity, and kinetic energy as in part (b).
ANSWER:Step 1 of 4
First show that the moment of inertia and kinetic energy of a flywheel can be written as and
.
The calculate the kinetic energy of the given steel flywheel at given speed.
Then we have to find out the mass and the radius of the aluminum flywheel.