moment of inertia by integration

821 Rectangle minus semi-circle | Moment of Inertia

Problem 821
Find the moment of inertia about the indicated x-axis for the shaded area shown in Fig. P-821.
 

821-rectangle-minus-semi-circle.gif

 

Area, moment of inertia, and radius of gyration of parabolic section

Situation
Given the parabola 3x2 + 40y – 4800 = 0.
 

Part 1: What is the area bounded by the parabola and the X-axis?
A. 6 200 unit2
B. 8 300 unit2
C. 5 600 unit2
D. 6 400 unit2
 

Part 2: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 15 045 000 unit4
B. 18 362 000 unit4
C. 11 100 000 unit4
D. 21 065 000 unit4
 

Part 3: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 57.4 units
B. 63.5 units
C. 47.5 units
D. 75.6 units
 

 
 
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