Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Determine the moment of inertia and the radius of gyration of the shaded area with respect to the $y$ axis.

Physics 101 Mechanics

Chapter 9

Distributed Forces: Moments of Inertia

Section 2

Parallel-Axis Theorem and Composite Areas

Moment, Impulse, and Collisions

Cornell University

University of Washington

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.

06:58

Determine the moment of in…

01:46

01:31

01:22

03:55

03:06

01:27

01:32

01:57

02:32

now, I asked to find the area moment and radio preparation about the Y axis for this shape. And we have all the dimensions. And so, um, the Y axis goes through the central rate of this piece and the central of this piece. So we just get these simple expressions here, and we wind up with I about why this access for this member is 10.67 inches to the fourth. Um, for this member, it's 5.33 interest of the fourth. They looked the same here, but I've drawn it out of scale. And in fact, this is much thicker than this. So this makes sense. And then these guys, basically we need the take the area moment about about why of its about to its central right. And we get this. And then we need to take punk, apply the area times the distance from the why access to the centrally and that I called the three and we can get that from the schematic in the book. And we also know that this one is gonna be the same because of symmetry about this, and so that these two each one has a area moment of 15.25 inches to the fourth. So our total area moment about the why access is, um this Plus this plus two times this and we get 46.5 inches to the fourth. Our area is again 18 interests squared, and our radius of gyration becomes 1.6 or seven inches.

View More Answers From This Book

Find Another Textbook

Numerade Educator

03:15

A worker uses high-pressure water to clean the inside of a long drainpipe. I…

03:58

The peripheral speed of the tooth of a 10 -in-diameter circular saw blade is…

07:36

A plastic film moves over two drums. During a 4 -s interval the speedof …

07:43

Nonlinear springs are classified as hard or soft, depending upon the curvatu…

02:33

Determine the force in members $G J$ and $I K$ of the truss shown. (Hint:

08:04

Determine the polar moment of inertia of the area shown with respect to $(a)…

04:58

Express the acceleration of gravity $g_{h}$ at an altitude $h$ above the sur…

02:54

The three blocks shown move with constant velocities. Find the velocity of e…

04:16

A recording tape passes over the $20-\mathrm{mm}$ -radius drive drum $B$ and…

05:50

A boat is moving to the right with a constant deceleration of $0.3 \mathrm{m…