Moment of inertia Definition and 1000 Threads

Homework Statement What is the moment of inertia round the axis of a cylinder length L, mass M and a linear distribution of mass with the radius R, zero at the center. Homework Equations Moment of inertia: ##I=mr^2#3 The Attempt at a Solution The density ρ=kr. what is k? the total mass is M...

Homework Statement Calculate the moment of inertia of a cube of mass M and edges d round an axiz, z, that passes in the middle. Then calculate around an axis parallel to the z axis and passing on one of the edges Homework Equations Moment of inertia: ##I=\int r^2dm## The Attempt at a...

Homework Statement The profiled steel I above is topped by a " profiled C ". Determine the moments of inertia of the structure composed by the axes central x and y through its geometric center C. Picture representing the problem: Homework Equations Profiled C and I information: The Attempt...

Homework Statement The problem Direct imgur link to problem: http://i.imgur.com/QCc0zj6.jpg Homework Equations \alpha = \frac{\tau_{net}}{I} I = \frac{1}{2}MR^2 \tau = rF = rmg The Attempt at a Solution I have figured that the moment of inertia of the entire system must be used for...

Homework Statement Usually in any question will the magnitude of the couple(friction) be given or is it possible to find the couple from the co efficient of friction between the rotating object and the axis ? Homework EquationsThe Attempt at a Solution

Homework Statement Two particles of mass m1 = 14 kg and m2 = 24 kg are connected by a massless rod of length 1.4 m. Find the moment of inertia of this system for rotations about the following pivot points. Assume the rotation axis is perpendicular to the rod. A) center of rod B) end of m1...

Homework Statement Three particles, each with mass m = 0.5 kg, are fixed on a uniform circular ring of mass M = 2 kg, radius a = 0.6 m and centre O, to form the corners of an equilateral triangle. What is the moment of inertia of this system? Homework Equations I = Σma2 The Attempt at a...

So the following question is attached (There is another thread with the same question but no solution to what I am asking on there) Now according to several solutions, apparently IYZ is equal to 0, and they reason this by saying that the geometry is symmetrical. However when looking at the...

Homework Statement What is the Moment of inertia of rod about an axis inclined? It is given as ## \frac{ML^2sin^2θ}{12} ## but how? Homework Equations I know MOI for axis passing through center along y-axis as ## \frac{ML^2}{12} ## The Attempt at a Solution Shouldn't it be ## \frac{ML^2}{12}...

Homework Statement Homework Equations W = Torque * distance 3. The Attempt at a Solution The net torque is 8*.09-11*.06 = .06, and the distance moved is 4pi, because 2 full rotations, but this is not one of the choices...

I have been trying this problem for a while and can't seem to figure it out: A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside radius. A resistive force f = 137 N (due to the ground) is applied to the rim of the tire. A force...

Hi, Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.

I have a question about body inertness. Is moment of inertia is unambiguous inertness characteristic?

Homework Statement Hi all, I just had a quick question regarding a problem that I have to write a lab report on. The problem involves solving for the moment of inertia of a system that involves a pulley with a hanging mass attached to a spool that turns a flywheel. The solution is supposed to...

Homework Statement I am trying to work the moment of inertia for a) rotating rod, axis through the centre of the rod http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3 b) Solid cylinder http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2 [/B] Homework Equations I = R^2 dM The...

Sorry to bring this question up again. @aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as: $$...

I had a discussion with my friend. He took an icecream stick and told me that if the stick was held horizontally the stick would break easily but if you held the stick vertically it would be difficult to break the stick. He said that vertically the moment of inertia is more. My question is that...

Homework Statement The L-shaped bar of mass m is lying on the horizontal surface when the force P is applied at A as shown. Determine the initial acceleration of point A. Neglect friction and the thickness of the bar. (Sorry, don´t know how to get you a better picture) L...

Homework Statement See the attached image. Homework Equations ##T = 1/2 \omega^2 I## The Attempt at a Solution So ##I_1,I_2,I_3## are just the moments of inertia of the object with regards to the 3 axes. Right? OK, then I intuitively assume that the total kinetic energy must simply be...

Homework Statement for this composite object, what moment of inertia needs to be used if you were to sum the moments about the centroid of the object, \sum M=I\ddot\theta Homework EquationsThe Attempt at a Solution is it the sum of the I_zfor a solid sphere and a solid cylinder

Homework Statement "a uniform steel rod of length 1.20 meters and mass 6.40 kg has attached to each end a small ball of mass 1.06 kg. The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. Find the moment of inertia of the ball-rod system." Homework...

A equilateral triangular lamina, has a moment of Inertia of I if the axis of rotation passes through the centroid of the triangle, perpendicular to it's plane. What is the moment of inertia of a regular hexagon(Again, through it's geometrical centre, perpendicular to the plane), provided that...

I am doing a mini hovercraft project. Regarding my design, I plan to place the fan (LIFT) in the middle of a rectangular styrofoam board (15 inches by 8inches). The position of my fan would be (x=7.5, y=4in); this would also be my center of gravity. My origin (coordinate) is at the corner of...

Homework Statement These are the pre lab tasks for my upcoming lab. Find the theoretical value for moment of inertia for a ring with off axis rotation using parallel axis theorem and outline procedure to obtain experimental value of I. During the lab we will be using a rotating platter with a...

Hello! Well, I am in trouble with this question for some time. I am making a simulator with autonomous cars and its movement is done applying constant impulses to the wheel. My question is: if the vehicle is in the intertia state and I start to apply this impulses, the vehicle will assume a...

I've been studying rotational motion for a while and I have no clue how moment of inertia plays a role in it. How would you define it? Often times, it's just described as resistance to change. Does that mean a high moment of inertia means a higher resistance to change or is it the other way...

I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane...

Homework Statement A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.9 kg and radius R = 0.22 m. The rods each have mass mr = 1.4 kg and length L = 0.83 m. 1) What is the moment of inertia of each rod about the axis of rotation...

Hello, sorry for this stupid question. I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value. I'm pretty sure it has to be MR^2/4, but I=\int r^2 dm \\ dm=(M/A)dS With A=\pi R^2/2 I compute...

Homework Statement I'm trying to solve for the area moment of inertia of a curved arc. To visualize this, it would be like a bent piece of cardboard (two arcs with two lines connecting them at their end points). I'm modelling the differences in area MOI with an increasingly curved piece of...

Homework Statement There are four solid balls with their centres at the four corners of a square of side a. The mass of each sphere is m and radius is r. Find the moment of inertia of the system about one of the sides of the square. Homework EquationsThe Attempt at a Solution I= 2 (two balls)...

Homework Statement 3.) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)...

Two rectangular objects, each 1.0 m by 3.0 m, are attached as shown. Each rectangle has a mass of 1.5 kg. Find the moment of inertia of the system about (a) axis A, (b) axis B, and (c) axis C. I have no idea what to do, any help is appreciated.

Consider a partially filled bottle of water. When it's tipped over and rotating about its pivot point where its edge touches the ground, it has an angular acceleration. Assuming the liquid is not viscous at all, so flows perfectly, at a given instant can it be considered to have a moment of...

Homework Statement So I generally understand how to solve the following problem. My only roadblock is that I am not sure I am solving the moment of Inertia correctly. I know that for a solid cylinder you would use I = 1/2mr^2, but I am not sure how if it has only one mass given of 10 kg, yet...

Hello, I am currently attempting to cover rotational motion using Halliday's Fundamentals of Physics. I understand very well the concept of moment of inertia as defined as the sum Σmi*ri2. However, the textbook argues that if there are too many particles, the moment of inertia can be defined as...

Lets say we are sitting on a horse at the edge of a merry-go-round. You move faster relative to a point near the centre of the merry go round. Now most of the mass of this merry go round is at the edge i.e at the horse. So the moment of inertia at the horse is less. Correct me if I am wrong.

What I have are two wheels, weight assumed at 50 kg overall for both, joined by an axle. The wheels are 900 mm apart from the centre of one tire to the centre of the other. The diameter of the tire is 690 mm. How do I calculate the moment of inertia in order to find the torque in the centre of...

For fun, I thought I would try to derive the moment of inertia of a square using different approaches (in each case, changing the differential area being integrated). Everything went well until I tried the approach of first considering the disk in the center of the square, then adding the bits...

Homework Statement Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center Homework Equations I = ∫rρdV The Attempt at a Solution I =ρ ∫r4πr2dr = ρ4π∫r4 Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5) And...

What is the mass moment of inertia about the longitudinal axis of the shape attached in this thread, but in 3 D? I found this "Handbook of Equation for Mass and Area Properties of Various Geometrical Shapes" which gives the mass moment of inertia of a regular octagon. I initially thought that...

If we have five identical rigid rods, each of length l and mass m, are connected together to form the system shown in the figure. The system may rotate about an axis passing through AB. The question is to find the moment of inertia of the system with respect to axis AB. I managed to find the...

Homework Statement I have a disk that can rotate about an axis at a radial distance h from the center of the disk. I am given a graph showing the the rotational inertia I of the disk as a function of the distance h from the center of the disk out to the edge of the disk. From the graph (see...

Hi! I got the task to determine the moment of inertia of a hollow cylinder, however it's not about just measuring the mass and the inner and outer radius and putting it into the right formula, instead I should roll it down an inclined plane. 1. Homework Statement I'm only allowed to use the...

Hello, I am trying to find the moment of inertia of a uniform rod, that has a mass added to it at some position along it's length, which is equal to the mass of the rod itself, and the axis of rotation is at one end. 1. Homework Statement A uniform, \mathrm{1.00m} stick hangs from a...

I am trying to learn to calculate collisions on the center of percussion of a rod. Can you tell me how to find the moment of inertia? Suppose we have a rod of length 1m and mass M = 12 kg., we know that ##I = 12 * 1^2 / 3 = 4## , if a collision takes place at the CoP ( at 0.166666 m from the...

Homework Statement 2-1. A constant torque of 4 Nm is applied to an unloaded motor at rest at time t = 0. The motor reaches a speed of 1717 rpm in 4 s. Assuming the damping to be negligible, calculate the motor inertia in Nm·s2. Homework Equations T = J(eff) * dw/dt J = kg*M^2 The Attempt at a...

I have done some extensive self study on MOI but I don't understand it's meaning in application. An example is imagine a stick of butter is dropped on the ground. Now ignoring friction and the other variables we can remove for learning purposes, let's assume the butter stick is kicked and it...

I want to calculate moment of inertia of an angle L bent in form of a parabola. The parabola is attatcehd to a H section bent in form of a circle such that the center of circle and focus of parabola lie at the same point. I want to know how to calculate the moment of inertia for the whole assembly

The problem is to show that the moment of inertia of a rectangular plate of mass $m$ and sides $2a$ and $2b$ about the diagonal is $\displaystyle \frac{2}{3} \frac{m a^2 b^2}{a^2+b^2}.$ I did it using the traditional definition of moment of inertia, that is, $$I = \int r^2 \, dm.$$ However, the...