Question

Find the radius of gyration with respect to its axis of the solid generated by revolving the region bounded by y=4x and y=x^2 about the y-axis if p is the density than the radius of gyration ?

          Find the radius of gyration with respect to its axis of the solid generated by revolving the region bounded by y=4x and y=x^2 about the y-axis if p is the density than the radius of gyration ?
        

Added by Jacob J.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the radius of gyration with respect to its axis of the solid generated by revolving the region bounded by y=4x and y=x^2 about the y-axis if p is the density than the radius of gyration ?
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Transcript

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00:01 Hi, in the given problem radius of gyration k y is equal to square root of iy over a where a is the area and then we'll find the area which is the moment the moment of inertia so let's find a which is the double increase from 0 to 4 for x and from y it is x squared to 4x 4x the row function dy d x which is equal to row 0 to 4 this is 4x minus x squared d x so on integrating this is for further integrating we get this as 32 over 3 row so that's the value of area a now all i y inertia moment of inertia is are x squared d a that is row 0 to 4 x squared to 4 x square to 4 x square d y d x so on solving this integral we have row 0 to 4 this is x square times 4x minus x square d x which is on integrating its value of 256 row over 5 so the radius of caration gai is equal to the formula is iy which is 256 row over 5, whole divided by 32 over 3.
01:58 So this gives us square root of 24 over 5...
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