Moment of inertia Definition and 1000 Threads

Homework Statement A thin uniform rod of mass (M) and length (L) is bent at its center so that the two segments are now perpendicular to each other. a. Find its moment of inertia about an axis perpendicular to its plane and passing through the point where the two segments meet...

Hi Guys, I'm having trouble finding the equivalent moment of inertia for a system. Basically it's a mass attached to a string, which is attached to a shaft. As the mass drops, the string unravels imparting some rotation on the shaft, this shaft rotates a small flywheel, and also rotates a...

If you have a roundabout spinning with a man standing on it close to the centre, and then he walks out towards the edge of the roundabout, angular momentum is conserved, but kinetic energy is not (the roundabout rotates with a smaller angular speed). I'd like to know where the kinetic energy in...

Homework Statement A solid ball of mass M and radius is connected to a thin rod of mass m and length L as shown. What is the moment of inertia of this system about an axis perpendicular to the other end of the rod? Image: http://imageshack.us/photo/my-images/35/helpfy.jpg/ Homework...

Homework Statement A uniform cylinder, of radius 2a and moment of inertia $2Ma^2$ is free to rotate about its horizontal axis. A light, inextenzible string is wound round the cylinder and a particle of mass m is suspended on its free end. If the system is released from rest, find the...

I'm doing an experiment and I have to calculate calculate rotational kinetic energy of this can rolling down an inclined plane. According to the equation, Er=1/2Iw^2, I=mr^2, and w=v/r (no slipping effect) right? but doesn't I=mr^2 apply only when the weight is evenly distributed throughout...

Homework Statement A wheel free to rotate about its axis that is not frictionless is initially at rest. A constant external torque of +44 N·m is applied to the wheel for 23 s, giving the wheel an angular velocity of +520 rev/min. The external torque is then removed, and the wheel comes to rest...

So I've been trying to derive the moment of inertia equation for a thin spherical shell and I've slammed into a dead end algebraically. I was able to derive an equation for a hollow sphere: I = (2/5) M (Ro^5 - Ri^5)/(Ro^3 - Ri^3) where Ro is the distance to the very outside of the sphere...

I got the algorithm to deal with every section profile. The software would calculate the area and the moment of inertia of any section or any combination of sections in different materials. Further more, I would develop it to deal with non-linear analysis finding the stress and strain on every...

Homework Statement part c and part d And the ans. a.)140 b.)130/21 c.)6.92M d.)150M/7 Homework Equations The Attempt at a Solution It seems the ans is wrong, I am not sure. Can you help me?

Static moment VS Moment of inertia -- what's the difference? What's the difference between moment of inertia and static moment? How does it differ in calculations?

To this shape http://img10.imageshack.us/img10/2301/nocalculations.jpg Uploaded with ImageShack.us I'm asked to calculate the estimate of the static moment of inertia of the planar shape towards the x axis, that goes through its center of gravity. And then I'm told that I'm asked for...

Homework Statement The first quadrant area bounded by the curve x^3+y^3=8 is rotated around y-axis to give a solid of rotation. The question asks for an integral which represents the solid's moment of inertia around the axis. My answer is: I_y=M\frac{\int_0^2x^2ydx}{\int_0^2x^2dx}...

Hi everybody: I can see that there are formulas to calculate the moment of inertia of a 2D Area (Second moment of area) here: http://en.wikipedia.org/wiki/Second_moment_of_area" In the same link, there is a formula to calculate the Inertia moments about a ROTATED AXIS (Axis Rotation)...

Guys i need a little help in finding the moment of inertia of a part of a machine which looks like the part of a torus as the arc of a circle.Can somebody help me out with it please?

Homework Statement Compute the moment of inertia around the z-axis of the solid unit box [0,1]x[0,1]x[0,1] with density given by \delta=x^{2}+y^{2}+z^{2}. Homework Equations I=\int\int\intr^{2} \delta dV The Attempt at a Solution I know that the distance r^{2} from the z-axis would...

i need to find the moment of inertia for a cardboard boomerang. what equation could i use?

set up a triple integral for the moment of inertia Iz for the region inside the sphere x^2+y^2+z^2=4a^2 and inside the cylinder x^2+y^2-2ax=0 so I draw my picture and convert to cylindrical coord. and i get an integral from 0 to sqrt(4a^2-r^2) an integral from 0 to 2acostheta and an...

http://img20.imageshack.us/img20/9443/ssssnm.png parallel and perpendicular axis theorem for moment of inertias So i solved the Moment of inertia for the large square through the perpendicular axis through a, (1/3)*M*(l^2), where l is 4a/2=2a, using the perpendicular theorem, Ixx+Iyy=Izz, we...

Find the moment of inertia of a wire, AB, of mass M and length pi*a, which is bent into a semicircle, about AB. Mr^2/b] [b]The mass of the wire is M=pi*a*m, where m is the mass per unit length of the rod. Then a small element, ds is regarded, of the circumference of the semicircle as being...

I'm basically just trying to find a list of all the shapes and their relative moment of inertia to each other. I want to see what shapes have more and what less, just to get a more intuitive sense to this subject. Does anyone show such a list, or maybe can just tell me of basic geometrical...

Homework Statement A wheel free to rotate about its axis that is not frictionless is initially at rest. A constant external torque of +43 N·m is applied to the wheel for 20 s, giving the wheel an angular velocity of +610 rev/min. The external torque is then removed, and the wheel comes to...

This a question that has been haunting me for some time now. Regarding the rotational motion of rigid bodies why wasn't the moment of inertia defined as the integral sum elements of infinitesimal mass time the radius from the axis of rotation rather than the radius squared. In this case the...

Not a homework question per se, but I'm having some issues with moments of inertia. Say I wanted to calculate the I for a ring. What I would do is: I = \int r^2dm m = \lambda L dm = \lambda dL I_{ring} = \int_{0}^{L}\lambda r^2dL And that would give the requiside mr2. My question...

Hi guys I am trying to find the moment of inertia of a thin triangle sheet as shown in the attached file, I couldn't so I looked at the solution and it said that x1 = ay/h and x2 = by/h. That is the only part I don't get, it seems to be some sort of ratio but I can't work out how or why its like...

Homework Statement This isn't a homework problem but rather a problem I need to solve for a personal project of mine. Basically I need to find the moment of inertia of the following: http://img860.imageshack.us/img860/3952/roboframe.jpg Uploaded with ImageShack.us The rotation is with...

Could anyone prove the moment of inertia of a thin walled hollow sphere using the y^2 + x^2 = r^2. I have only studied up to single variable calculus. I can take regular integrals but not multivariable integrals. I don't want to use the angle method or any polar coordinate systems except in the...

Homework Statement I am trying to find an equation relating the acceleration (not angular acceleration) to the moment of Inertia. I have a question that says a coin and a ring have same mass and same radius, which one would reach the bottom first if they were released from the top of an...

I was wondering if there is any way to prove the moment of inertia of a thin walled hollow sphere by using y^2 + x^2 = r^2 instead of using the angle method. I want to use a Cartesian coordinate system not a polar coordinate system.

Homework Statement Homework Equations i guess its r=sqrt(I/A) where A is the area of the circle thing and I is the moment of intertia. The Attempt at a Solution I guess I'm just having trouble getting I. A is 33pi

We've always been using mm^4, but I see in my answer book (answer written below) that one solution says R^4. Is it the same thing, just that R^4 is used for a circle? The measurement in my exercise are in mm. I did get the answer, I just wasn't aware I was supposed to write it in terms of R^4.

Homework Statement Find the moment of intertia of a pendulum, consisting of a disc free to spin attached to a rod that is hinged at one end. Homework Equations Moment of intertia of rod hinged at end = (1/3)Ml2 Moment of intertia of disc = (1/2)mR2 + ml2 The Attempt at a Solution...

Statics, moment of inertia simple square-shape...need help (no calculus) Homework Statement Calculate the moment of inertia to the central axes Xc and Yc for the sketched cross-section. Xc = 33.9 mm Yc = 150 mm http://img822.imageshack.us/img822/1303/97823499.jpg Uploaded with...

Hi! I've got a problem with this: Count moment of inertia for rectangular plate a x b, if you know that moment of inertia of thin rod is \frac{1}{12}ml^2 . Do not use integrals!, others mathematical functions required (I can proof this moment by integrals, but this is not issue). I know that...

Homework Statement See attachment or here http://i.imgur.com/zBDa0.png Homework Equations Torque = FR Moment of Inertia of Rod at End = I = 1/3 ML ^2 The Attempt at a Solution http://i.imgur.com/3Avqh.png

So I understand that Ix resistance to rotation around the X axis, Ixc is resistance to rotation around the center of gravity of the shape on its X axis, and Io I was told is also resistance to rotation around the object's center of gravity. So, I'm completely confused as to the difference...

Hi, I just got of a test that had a question about moment of inertia on it. The question "Calculate the moment of inertia of a thin uniformed disk that is being rotated about an axis of rotation". This axis is halfway between the center of the disk and the outer perimeter. The mass of the disk...

1. 2. I = (x/x) M L ^ 2 3i honestly have no idea where to go with this. i do have an attempt so please don't laugh. I took the (L) for the moment for the rod = 3.4 m and divided it into 2 parts. R sub 1 and R sub 2. With R sub 2 on half of R sub 1. The equation i got using the R...

Homework Statement Four small spheres, each of which you can regard as a point of mass 0.200kg , are arranged in a square 0.400m on a side and connected by light rods . Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an...

Homework Statement Find the moment of inertia Ix of particle a with respect to the x-axis (that is, if the x-axis is the axis of rotation), the moment of inertia Iy of particle a with respect to the y axis, and the moment of inertia Iz of particle a with respect to the z axis (the axis that...

Homework Statement Small blocks, each with mass m, are clamped at the ends and at the center of a rod of length L and negligible mass Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end...

Hello, Calculating the moment of inertia of a solid uniform sphere about it's center I get (3/5) Ma2. I know I am supposed to be getting (2/5) Ma2. I am using a differential volume dm as 4*pi*rho*r*r*dr, where rho is density, and r is the distance from the center to the differential volume...

Homework Statement Three particles of mass m are placed at A=(-a, -a), B=(a, -a) and C=(0, a) Find the moment of inertia for an axis along the z-axis through the origin Homework Equations I = m((rA)2 + (rB)2 + (rC)2) The Attempt at a Solution I calculate that: (rA)2 =...

I am confused with how to find moment of inertia of composite example. Like a hollow shell having one disc at each end and a shaft in the centre. How to find out Moment of Inertia if Force is applied tangentially on the shell and if force is applied tangentially on the shaft. Should I sum up...

Hey, I was doing some problems involving finding the moment of inertia of a spun spandrel, and I came across the idea of using the centroid to find the moment. For example, if you have a parabola, find the centroid. If you're rotating around the x-axis (y=x^2), then find y_bar and multiply...

Homework Statement Experiement 1: One student sits on a stool that rotates freely. He holds a 5-kg mass in each hand. Initially, the student has a angular velocity of 5 radians/sec with his arms in his lap. Question: In exp 1, with his arms outstretched, the student drops the...

Hello there, i have a problem with calculating the moment of inertia for the object on the picture. There are two cases I'm observing. In the first case, the obect rotates around the axis located in the center of the big circle, and the little circle can't rotate around the axis located in...

Homework Statement A solid, horizontal cylinder of mass 16.3 kg and radius 1.44 m rotates with an angular speed of 2.24 rad/s about a fixed vertical axis through its center. A 0.239 kg piece of putty is dropped vertically onto the cylinder at a point 0.624 m from the center of rotation...

Hi, one of my vac work questions is: A lamina has density d(x,y) = x^2 + y^2 and is defined by -2<x<2 ; -3<y<3. Calculate the moment of inertia about an axis perpendicular to the lamina through the point (1,1). I'm confident that I find Ix which is equal to the double integral of the...

Homework Statement Calculate the moment of inertia to the Y and X axis Diagram attached. Homework Equations Everything is in the diagram...there's no need to use calculus, just the formulas for geometrical shapes for moment of inertia and center of mass... Answers are Ix =...