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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

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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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whereas to determine by direct integration The second moment of area we expected the X excess Tom and that area is bombed and bordered by this function here. We know, um the X equals a wise bs. OK equals B over eat in agro that we need to do to find the second moment very about the X axis is why squared over the area. And that area goes from y equals zero to our function here. Why of X and X goes from zero to a cranking through those integral we get that I set backs equals E Q minus one all over nine e cube times a B cube. And if we, um, calculate this numerically, we get that we have 0.106 a. B cube is our answer.

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