Chapter 8. The parallel-axis theorem (8-8)

Question

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{"title":"Moment of inertia of an object for a certain rotation axis","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,22,30,62\"}]"} {"title":"Moment of inertia of the same object for a second, parallel axis through its center of mass","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"78,23,102,61\"}]"} {"title":"Distance between the two parallel axes","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"255,20,284,59\"}]"} {"title":"Mass of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"205,23,251,63\"}]"}

Question

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{"title":"Moment of inertia of an object for a certain rotation axis","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,22,30,62\"}]"} {"title":"Moment of inertia of the same object for a second, parallel axis through its center of mass","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"78,23,102,61\"}]"} {"title":"Distance between the two parallel axes","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"255,20,284,59\"}]"} {"title":"Mass of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"205,23,251,63\"}]"}

Question

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{"title":"Moment of inertia of an object for a certain rotation axis","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,22,30,62\"}]"} {"title":"Moment of inertia of the same object for a second, parallel axis through its center of mass","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"78,23,102,61\"}]"} {"title":"Distance between the two parallel axes","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"255,20,284,59\"}]"} {"title":"Mass of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"205,23,251,63\"}]"}

Question

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{"title":"Moment of inertia of an object for a certain rotation axis","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,22,30,62\"}]"} {"title":"Moment of inertia of the same object for a second, parallel axis through its center of mass","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"78,23,102,61\"}]"} {"title":"Distance between the two parallel axes","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"255,20,284,59\"}]"} {"title":"Mass of the object","description":"Mass of the object","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"205,23,251,63\"}]"}

Review

WIth regard to the the parrellel-axis theorem, if the distance between the two parrallel axes of an object, such as a hoop, is \(h\) and the mass of the object is \(M\), the relationship between the two values of moment of inertia is: