Moment Of Inertia Of A Hinged Door

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Moment of inertia of a hinged door.

Homework equations i x 2dm the attempt at a solution b the way i set it up was that i made into strips of length h height and width dr. The width of the door is unnecessary. Id moment of inertia of mass of door at door s centroid if door was a point 16cm from edge of door m r 2 with r being distance of centroid from a point 16cm from edge of door. Dm λhdr where λ is mass over the length h.

The moment of inertia of the door is then r 2 d m. The moment of inertia can be found by breaking up the object into little pieces multiplying the mass of each little piece by the square of the distance it is from the axis of rotation and adding all these products up. A uniform thin solid door has a height of 2 2 m a width of 0 87 m and a mass of 23 kg. A dumbbell has a connecting bar of negligible mass.

Find the location of its center of mass x cm if the end masses m 1 and m 2 are 5 0 kg and 10 0 kg respectively. Are any of the data unnecessary. Find the moment of inertia for rotation on its hinges. What is the moment of inertia of the door about the axis through its hinges.

The moment of inertia of an infinitesimal mass element d m is d m r 2 in which r represents the distance from the mass element to the axis about which we are considering the moment of inertia. Moment of inertia denoted by i measures the extent to which an object resists rotational acceleration about a particular axis and is the rotational analogue to mass mass moments of inertia have units of dimension ml 2 mass length 2 it should not be confused with the second moment of area which is used in beam calculations the mass moment of inertia is often also known as the. What is the moment of inertia of the door about hinges. Find its moment of inertia for rotation on its hinges.