8-10. calculate the moments of inertia with respect to both centroidal axes for the areas shown. 80 mm (a) 2/2 3D aud sym 300 mm 100-mm-diameter hole (b) 180 mm 600 mm
8-10. calculate the moments of inertia with respect to both centroidal axes for the areas shown. 80 mm (a) 2/2 3D aud sym 300 mm 100-mm-diameter hole (b) 180 mm 600 mm
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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Transcribed Image Text:**Transcription for Educational Website:**
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**Topic:** Calculating Moments of Inertia for Areas
**Problem 8-10:** Calculate the moments of inertia with respect to both centroidal axes for the areas shown.
**Diagrams:**
1. **Diagram (a):**
- Features a symmetric shape resembling a cross with semicircular cutouts on the top and bottom.
- Dimensions:
- Total width: 80 mm
- Total height: 80 mm
- Diameter of each semicircular cutout: 45 mm (typical)
2. **Diagram (b):**
- Features a rectangular shape with a central circular hole.
- Dimensions:
- Rectangular height: 600 mm
- Rectangular width: 300 mm
- Diameter of the central circular hole: 100 mm
- Distance from the top edge to the center of the hole: 180 mm
The objective is to determine the moments of inertia about the centroidal axes for each shape.
**Page Reference:** 2/2
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Use these diagrams to understand how geometric modifications such as cutouts can affect the calculation of moments of inertia in engineering applications.
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Step 1: Given data
VIEWStep 2: Calculation of CG for given shaded area
VIEWStep 3: Calculation of M.O.I of shaded area w. r. to colentroidal X axes
VIEWStep 4: Calculation of M.O.I of shaded area w. r. to colentroidal X & Y axes
VIEWStep 5: Calculation of CG for given shaded area
VIEWStep 6: Calculation of M.O.I of shaded area w. r. to colentroidal X axes
VIEWStep 7: Calculation of M.O.I of shaded area w. r. to colentroidal Y axes
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