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

Physics 101 Mechanics

Chapter 9

Distributed Forces: Moments of Inertia

Section 1

Moments of Inertia of Areas

Moment, Impulse, and Collisions

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

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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and this problem was to determine the second moment of area by direct integration of about the X axis of an area defined by this function here. We can't I know that he can determine that K equals B over a squared by knowing that X equals zero. Why is be, And then we just need to set up our integration. And actually, I have the wrong letter here. So that's ice of X on. And that's an in agro of why squared over the area of the region that were interested in. And that region is given boom from zero to y of X and from X goes to zero a. So if we can't crank through the calculus here we get that I of X equals a B cubed all over 21.

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