Moment of inertia Definition and 1000 Threads

Homework Statement Hello, I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1. Known variables: L, D, P, t Dependent variables: T2, L2 Design variables: T1, L1 Homework Equations L2 = L - L1 T2 = T1 - t Standard...

Homework Statement Show that the moment of inertia of a hollow cone of mass M, radius R, and height h about its base is ##\frac{1}{4}M(R^2+2h^2)## Homework Equations ##I=\int r^2dm## where r is the perpendicular distance from the axis Surface Area of a cone ##= \pi R (R^2+h^2)^{1/2}## The...

Homework Statement String is wrapped around two identical disks of mass m and radius R. One disk is fixed to the ceiling but is free to rotate. The other is free to fall, unwinding the string as it falls. Find the acceleration of the falling disk by finding the lagrangian and lagrange's...

Homework Statement The moment of inertia for a perpendicular axis through the center of a uniform, thin, rectangular metal sheet with sides a and b is (1/12)M(a2 + b2). What is the moment of inertia if the axis is through a corner? The answer is given as this was a powerpoint lecture and it...

is there a directly knowing the moment if the moment of inertia would be lower for an object? I am emphasizing on knowing the value of the constant value. For a sphere is 2/5 and for a cylinder 1/2, this constant values will be placed at c of cMR^2 without directly going into calculus. A...

Homework Statement You are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.600 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at...

Homework Statement We consider a yo-yo rolling down an incline, sloping with angle θ relative to horizontal. The yo-yo starts a distance d up the incline. The string is attached to a hook further up the incline, in such a way that it unwinds as the yo-yo rolls down. The yo-yo can be thought of...

Homework Statement In the first photo , i was told that the I represent the moment of inertia about the neutral axis ... But , in the 2nd photo , i found that the author calculate the moment of inertia about the x-axis (parallel to neutral axis ) and y -axis ( perpendicular to neutral axis) ...

Homework Statement As shown in image. 2. Homework Equations Moment of inertia of pulley = 1/2*M*R^2 Moment of inertia of rod (about end) = 1/3*M*L^2 Acceleration of end of rod in theta direction = L*α Acceleration of end of rod in radial direction = L*ω^2 The Attempt at a Solution...

Homework Statement Not sure if this is advanced, so move it wherever. A certain rigid body may be represented by three point masses: m_1 = 1 at (1,-1,-2) m_2 = 2 at (-1,1,0) m_3 = 1 at (1,1,-2) a) find the moment of inertia tensor b) diagonalize the matrix obtaining the eigenvalues and the...

Hello all, and forgive me if I'm making newbie mistakes as I haven't posted here much. I realize this appears to be a homework assignment, but it is not. I am trying to develop an easy method for determining the actual moment of inertia for real wheels, for bicycles and other vehicles. I...

I remember my teacher saying it to be the axis along the centre of mass but the centre of mass has all the mass concentrated in it and hence moment of inertia should increase as moment of inertia is proportional to mass?

Homework Statement [/B] There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...

Sorry for my english at the beginning. :) I am not really into academic(physic) english. 1. Homework Statement Picture of problem : http://screenshot.sh/ouZAbUeL9Qzmj We have got a desk,mass m1, length L1 and thickness d, and L1>>d. One of it's ends is angled by 45 degree. At the beginning it...

Hello everyone, currently working on a physics project. I was very curios about waterwheels and actually have an overshot waterwheel setup. I was testing how the efficiency of a waterwheel would be effected by the drop height of water onto the waterwheel. Do any of you have any idea how I can...

Find the moment of inertia of a disc of mass m and radius r with a point mass of m on its circumference. i can't work this out can someone help me. i can work out that the moment of inertia of the disc is 1/2mr^2 but i don't know what to do with the point mass. i think it could have to do with...

Moment of inertia is supposed to be defined with respect to a rotational axis such that for a system of point masses, I=∑miri2 where ri 's are the perpendicular distances of the particles from the axis. However, in some derivations of the virial theorem (like the one on wiki), the so-called...

Homework Statement In the question , the author calculated the Ixx and Iyy , but he used the greater value (Ixx) in the calculation to calculate the shear stress , why did he do so ? why the greater value is used ? Homework EquationsThe Attempt at a Solution

Hi everyone! Please help, I have spent a considerable time to understand the two concepts and still this is nagging at me... I am relating to Structural Engineering, just to let you know guys. My question is .. Moment of inertia is about distribution of mass, the further away from the axis the...

a uniform annulus consists of disc of radius 3 meters with a disc of radius 1 meters removed from its center. the mass of the annulus is m. Prove that the moment of inertia of the annulus about an axis through its center is 5m.

What is the moment of inertia of massless (ideal) pulley that has a string attached to its center and a mass m attached to that string? If this pulley were hanging from a massless rope that was attached on one side to the cieling and the other side had a tension of mg, what would be the...

Homework Statement A clock balance wheel has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 10.0 g is concentrated around a rim of radius 0.600 cm. a) What is the wheels moment of inertia? kg m^2 b) What is the torsion constant of the attached spring? N m /...

Hi Unit of 'moment of inertia' is kg.m^2, Which I know. But about Inertia itself, is it a quantity phenomenon or quality phenomenon? What is it's unit?

Hello i have known moment of inertia to be kg mm2 i.e. the product of mass and distance but i was looking at the euler buckling formula and it has moment of inertia in it which has units of mm4.whats the differnece between the two inertias.please help

Hi Assume a Electropump which motor's moment of inertia is A and pump's moment of inertia is B. How can calculate Electropump's moment of inertia? Is it A+B or A*B?

I am trying to determine if a function I have is working correctly. The function computes the moment of inertia for a polygon. To test the function I created a polygon that has 4 points and represents a square of 4 units by 4 units. The answer I am getting is 32. I believe the answer should be...

Homework Statement A massless rod of length L connects three iron masses. If the first mass (at x=0) has a mass of 1.90 kg and the second mass (at x=L) has a mass of 8.77 kg and the third mass (located at the center of mass of the system) has a mass of 148 kg, what is the moment of inertia I...

Homework Statement we know that the moment of inertia is given by the formula of I = (ab^3) / 12 + A(y^2) ... why in the second photo , the author make it as I = 1443333- A(y^2) ? what is teh purpose of doing so , i don't understand ... Homework EquationsThe Attempt at a Solution

Homework Statement I am currently doing a lab investigating the relationship between the moment of inertia and speed. I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through...

hello all, I am currently doing a lab investigating the relationship between the moment of inertia and speed. I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through...

I know the moment of inertia for both a solid sphere and a hollow sphere is , but my teacher has derived a moment of inertia of the sphere but am not sure about what axis she was deriving it , and she got this answer 3/5 MR^2

I thought moment of inertia depends on mass of the object and also its shape. But prof Lewin says it doesn't depend on mass. See this video:

Homework Statement Homework Equations rotational kinetic energy = 0.5 I ⋅ M ⋅ ω², where I is the moment of intertia, M the mass and ω the angular speed The Attempt at a Solution T = period of revolution K = kinetic energy associated with rotational moviment Since T increases with time...

Homework Statement You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.700 kg . 1What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod? Express...

Ive got the following disk I am attempting to find the torque required to turn it 1/4 turn in 1/4 second. Am I correct when I am considering I(D)=1/2mr^2 as its a disk, and I(d)=mr^2? and The final moment of inertia to be I(D)+I(d)? Here is the disk I am speaking of...

Homework Statement The rope doesn't slide on the pulley, it's mass is negligible and it doesn't stretch .The pulley's moment of inertia is 0.00300 kg * m^2 with a radius of 10 cm. As the first mass goes down the rope's friction generates a moment of force of 0.150 N*m opposed to the angular...

Homework Statement Determine the location of y of the center of mass G of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3 kg and the mass of the semicylinder is 5 kg. Homework Equations -parallel...

So the moment of inertia or a ring is MR2 I don't understand why. Here is my reasoning Consider this shape (the ball is a point), the moment of inertia is MR2, there I agree but now what happens when you add another point on the other side since I = ΣMR2 then this is 2MR2 What about a...

For this problem, I don't understand how can the system be at rest and immediately after placing the mass, to move with constant speed. But anyways, can you tell me please how to proceed? On the hanging mass, there is mg acting and T the tension of the rope. On the flywheel, the tension of the...

1. Homework Statement In each question: you place mass m on the mass holder, and released the system from rest. The system includes the long rod with two point masses on it (see the picture next to the list of equipment). Since this is a rotational and translational motion, I set up two...

Homework Statement Find the moment of inertia of a spherical shell Homework EquationsThe Attempt at a Solution So I've been mulling over this for about two hours now and haven't figured out where I've made a mistake. Here's what I've done: I know I can do the integral by doing ##\int ^{r}...

Homework Statement A rigid body is made of three identical thin rods, each with length L = 0.530 m, fastened together in the form of a letter H, as suggested by the figure here. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body...

Homework Statement Determine the moment of inertia of the shaded area about the x-axis. Homework Equations I(x)= y^2dA The Attempt at a Solution In order to determine the moment of inertia of the shaded area about the x-axis I first looked at the portion above the x-axis, integrate it with...

Homework Statement In the figure, a wheel of radius 0.42 m is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a 2.7 kg box that slides on a frictionless surface inclined at angle θ = 28 owith the horizontal. The box accelerates down the...

Homework Statement Determine the moment of inertia of the shaded area about the x axis.[/B]Homework Equations Ix=y^2dA The Attempt at a Solution Okey so I now get how to do this the standard method. But I want to know if the method I tried is correct as well or where my mistake lies. My...

Homework Statement Landau&Lifshitz Vol. Mechanics, p101 Q1 Find the moment of inertia of a collinear set of molecules Homework Equations I=sum m_i*(r_i^2) The Attempt at a Solution r_i= r_i'-r_cm where r_cm=sum m_i*r_i/sum m_i I=sum m_i r_i^2 I= 1/M sum m_i m_j (r_i' - r_cm)^2 I=1/M sum m_i...

Homework Statement Two identical rods, each with mass 5.00 kg and length 2.00m are welded as shown in the figure. If the moment of inertia of a rod about an axis passing through its center is Icm = 1/12ML2, what is the moment of inertia of the system of rods about an axis perpendicular to the...

Homework Statement The nucleus dysprosium-160 (containing 160 nucleons) acts like a spinning object with quantized angular momentum, L2 = l(l + 1) * h_bar2, and for this nucleus it turns out that l must be an even integer (0, 2, 4...). When a Dy-160 nucleus drops from the l = 2 state to the l =...

I'm currently completing an Atwood Machine Experiment with two 100g weights on either side of the pulley, with a variance in weight created by attaching dimes and pennies to either side of the weights. The point of the experiment is to validate: (m1 – m2)g = (m1 + m2 + I/R2) Homework Statement...

Homework Statement Hi everyone! I'm preparing an exam and reviewing some old problems until then, to clear up some misconceptions I might have! A stiff massless bar is frictionless rotatable about a point O. Two mass points m1 and m2 are fixed at its ends, respectively at distances d1 and d2...