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Determine by direct integration the moment of inertia of the shaded area with respect to the $y$ axis.

Physics 101 Mechanics

Chapter 9

Distributed Forces: Moments of Inertia

Section 1

Moments of Inertia of Areas

Moment, Impulse, and Collisions

Cornell University

Simon Fraser University

University of Winnipeg

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

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Determine by direct integr…

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who has to determine by direct integration the moment of inertia of the area. Actually, the second moment of area of the shaded area respect to the Y axis and that area is defined by was bordered by this function. Y equals K times quiet the X minus a cube. We know that at X equals three a. Why is be so that kay must be be all over eight a cube. The integral we need to do to get the, um, area moment The second moment of area, I said, Why is to integrate X squared all over the region of interest? And that region goes from zero to why have X and then X goes from a to three A. In this case so we can crank through those in a girls and we get that I supply equals 103 over 30 times a cube. Be

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