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Find the indicated moment of inertia or radius of gyration.Find the moment of inertia (in $\mathrm{kg} \cdot \mathrm{m}^{2}$ ) of a rectangular door $2 \mathrm{m}$ high and $1 \mathrm{m}$ wide with respect to its hinges if $k=3 \mathrm{kg} / \mathrm{m}^{2}$ (See Exercise 22.)

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 5

Moments of Inertia

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02:01

Finding moments of inertia…

01:16

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03:49

(II) When discussing momen…

05:52

Center of mass, moments of…

02:44

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The moment of inertia abou…

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$A$ 25 $\mathrm{kg}$ sol…

so we can draw the store we have. And we have two bars. And we know that this distance here is considered out so we can consider the door to be made out of a large number of thin horizontal rods which, uh, this is an attempt that, uh, detail ing that. And, ah, with each of the length of El equaling 1.0 meters, so we can say that is there is rotating about one end. This would be the axis of rotation essentially, because when you open the door, this would this is how this is the axis about which it would rotate. We can You can see these two of these rods in this diagram, and it would simply be, ah, large number of thin horizontal rods all parallel to one another. So we can say that the moment of inertia of one of these rods would be equal to 1/3 time's initial l squared where, um, sub I is the mass of one single rod, so we consider it for a collection of identical rods all parallel to one another. The moment of inertia of the door would then be equal to the sum of 1/3. I'm sub I l squared, which would be equal to 1/3 times the mass of the door. L squared because the sum of all of the masses of these identical rods would be equal to the mass of the door. So we can say that the moment of inertia of the door would then be equal to 1/3 times 19 0.0 kilograms multiplied by 1.0 meters quantity squared. And so the moment of the moment of inertia for the door would be equal to 6.3 approximately kilogram meters squared. This would be our final answer. That is the end of the solution. Thank you for watching.

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