Obtain the moment of inertia () of the flywheel from its dimensions (see figure below). Note that the flywheel is two cylinders of diameter 0.03086 m and one cylinder of diameter 0.2008 m. (For uniform cylinders, / = 1/2(MR)) Since the masses are unknown, express the mass as the density (p) times the volume. Each part of the flywheel is made of the same material so there is only one density. You should now have an expression for the density in terms of I, the two diameters, the two thicknesses, and constants. 0.0520 m 0.03086 m 0.2008 m 0.0155 m
Obtain the moment of inertia () of the flywheel from its dimensions (see figure below). Note that the flywheel is two cylinders of diameter 0.03086 m and one cylinder of diameter 0.2008 m. (For uniform cylinders, / = 1/2(MR)) Since the masses are unknown, express the mass as the density (p) times the volume. Each part of the flywheel is made of the same material so there is only one density. You should now have an expression for the density in terms of I, the two diameters, the two thicknesses, and constants. 0.0520 m 0.03086 m 0.2008 m 0.0155 m
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![### Educational Resource: Calculating the Moment of Inertia of a Flywheel
#### Problem Statement:
Obtain the moment of inertia (I) of the flywheel from its dimensions. Note that the flywheel consists of two cylinders with a diameter of 0.03086 m and one cylinder with a diameter of 0.2008 m. For uniform cylinders, the moment of inertia I is given by the formula:
\[ I = \frac{1}{2} (MR^2) \]
Since the masses are unknown, express the mass as the density (ρ) times the volume. Each part of the flywheel is made from the same material, so there is only one density. The objective is to derive an expression for the density in terms of I, the two diameters, the two thicknesses, and constants.
#### Diagram Description:
- **Left Diagram**:
- A front view of the flywheel.
- It shows two concentric circles indicating two cylinders.
- The inner circle (smaller cylinder) has a diameter of 0.03086 m.
- The outer circle (larger cylinder) has a diameter of 0.2008 m.
- **Right Diagram**:
- A side view of the flywheel.
- It shows both cylinders with thicknesses.
- Thickness of the larger cylinder: 0.0520 m.
- Thickness of the smaller cylinder: 0.0165 m.
The diagrams visually represent the dimensions required to compute the flywheel's moment of inertia using the provided formula and conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc583f9a-3f96-41e1-921f-9fa915d315b1%2Fea682d8f-490c-453f-99b8-cbade1bf275b%2F7nlwki3_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Calculating the Moment of Inertia of a Flywheel
#### Problem Statement:
Obtain the moment of inertia (I) of the flywheel from its dimensions. Note that the flywheel consists of two cylinders with a diameter of 0.03086 m and one cylinder with a diameter of 0.2008 m. For uniform cylinders, the moment of inertia I is given by the formula:
\[ I = \frac{1}{2} (MR^2) \]
Since the masses are unknown, express the mass as the density (ρ) times the volume. Each part of the flywheel is made from the same material, so there is only one density. The objective is to derive an expression for the density in terms of I, the two diameters, the two thicknesses, and constants.
#### Diagram Description:
- **Left Diagram**:
- A front view of the flywheel.
- It shows two concentric circles indicating two cylinders.
- The inner circle (smaller cylinder) has a diameter of 0.03086 m.
- The outer circle (larger cylinder) has a diameter of 0.2008 m.
- **Right Diagram**:
- A side view of the flywheel.
- It shows both cylinders with thicknesses.
- Thickness of the larger cylinder: 0.0520 m.
- Thickness of the smaller cylinder: 0.0165 m.
The diagrams visually represent the dimensions required to compute the flywheel's moment of inertia using the provided formula and conditions.
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