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Determine the moment of inertia for the shaded area about the $y$ axis.

$I_{y}=53332821 \mathrm{mm}^{4}$

Physics 101 Mechanics

Chapter 10

Moments of Inertia

Motion Along a Straight Line

Motion in 2d or 3d

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

University of Winnipeg

Lectures

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In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

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In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

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Determine the moment of i…

the moment of inertia about the Y axis is equal to the integral of X squared d A The d a was will be The area of the shaded rectangle is gonna be, uh, are let's see, 200 minus y times, dx and why we already have given as a function. So we'll substitute Why in for are integral when we get that The moment of inertia about the why is X squared It was 200 minus 1/50 x squared dx, further simplifying that we have an integral And then, um, we're gonna set our bounds here, so you're gonna be X bound, so it's gonna be negative. 100 to 100 is 200 x squared minus 100 or 1/50 x to the fourth DX. Let's integrate that and we have Let's see 1/3. Or I could just write 200 over three x cubed minus 1/5 times 50 to 50 x to the fifth immigrated from negative 100 to 100. So, um, when we saw that we get that the inertia moment of inertia about the Y Axis Sequels of 53.3, three times 10 of sixth millimeters to the fourth

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