Inertia Definition and 1000 Threads

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 I am stuck over a classical mechanics problem. I tried to solve it, but after having solved the first point, I got stuck on the second one. Here is the problem: >A mechanical structure is composed by 4 rigid thin bars of length $\ell = 8\ m$, mass $m = 5\ kg$ each one. Those...

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...

Hello, I am trying to establish what the moment of inertia is for this cantilever beam as well as the maximum strain. General formals preferred. Thank you

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...

I have a question on finding the inertia of a rod with a pivot point somewhere along it's length. So the inertia of a rod is IStick cm = 1/12 *m*L2 Does L2 = (2L/3)2 = 4L2/9 -> 1/12 *m*[4L2/9] or is it something like m*L2/12 + m* (2L/3)2? If it's the second one then may I ask why it's that...

Homework Statement A large wooden turntable in the shape of a flat disk has a radius of 1.50 m and a total mass of 100 kg. The turntable is initially rotating about its vertical axis through its centre with an angular velocity of 2.50 rad/s. From a very small height a 100 kg sand bag is...

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...

Hi, this is a question from a previous past paper that I am having trouble with. Am I meant to just use the number of teeth from each gear to find a ratio and use this to find the effective inertia at point C. Then use this to find a torque and take away the torque of the constant load. My exam...

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...

Hi can anyone help me with this question on inertial forces in gears? Cheers Ali :)

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 This is a question I have for a presentation on rotational motion: "A solid cylinder rolls down an incline faster than a hoop [or say an open cylinder], whether or not they have the same mass or diameter. The hoop has greater rotational inertia relative to its mass than a...

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...

Hi everyone, I have always been confused by momentum and linear inertia. What exactly is the difference between them? Aren't them both resistance to change in motion? Its hard to explain what I am confused with so here's an example: if there are 2 moving cars traveling at the same speed and car...

I am conducting an experiment that rotates a sealed donut cylinder to investigate amongst other things the inertia of the contained fluid. Process I rotate the cylinder to a set speed (assuming that the viscosity of the internal fluid will end up rotating the fluid to solid body rotation) then...

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 =...

Hello! Before I start I want to apologize for my english and not having a scanner (lol). I'm calculating the torque needed to rotate a wheel* around its own axis from above, ( see the link at the end of post). I have quite an good idea to how I'm supposed to calculate it but I feel that...

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...

Can any object have moment of inertia greater than that of a hoop?

Homework Statement Hi everybody! I know that is a classical problem, but I haven't been able to find an answer to my questions in the other threads so here we go: We have a yoyo made of 3 aluminium disks (density ρ). The two side disks have a radius R and thickness D, and the middle disk has...

Homework Statement http://i.imgur.com/7ZRsVj5.png Homework Equations I can't apply correct method ! The Attempt at a Solution In bigger figure, i cut into 8 equal parts.So , total moment of inertia=8 I But it's wrong ! I know it's wrong because i can't able to find angle between any two...

So in this problem there's a lot of leeway as far as parameters go. The numbers I give for weights, dimensions, etc, may not be super realistic, but that's not too important to me because I can plug in realistic numbers later. I more of need help understanding the concept of moments of inertia...

Homework Statement A) [/B]Consider a hollow sphere of uniform density with an outer radius R and inner radius \alpha R, where 0\leq\alpha\leq1. Calculate its moment of inertia. B) Take the limit as \lim_{\alpha\to1} to determine the moment of inertia of a thin spherical shell. Homework...

Homework Statement Homework Equations I = (1/3)ML2 Parallel axis theorem: Inew = Iold + mr2 The Attempt at a Solution I already solved part a) and I got (1/12)ML2. For b), I get that I have to use the parallel axis theorem but I don't know how to go from there. We have not gone over this...

Hello Forum, I have read Einstein famous thought experiments about the elevator. 1) Being inside an elevator accelerating upward in absence of a gravitational field is equivalent to being inside the same elevator at rest inside a homogeneous gravitational field. 2) An elevator in free fall...

Assume that a motorcycle of mass m has two wheels that are equidistant from its centre i.e the force on each wheel is m*g/2. If the motorcycle accelerates forward, will the two forces on each wheel (measured instantaneously) remain the same? If not, how can one mathematically describe the...

Hi, I've been always using eq. I=Pi*(D^4-d^4)/64 to find moment of inertia of a pipe. Recently I've seen that moment can be in different directions, and then it is expressed differently. So what is the difference between Ixy and Iz?

Homework Statement My textbook says that internal forces have no effect on an object's motion and that external forces are required to change the motion of an object. But, we looked at an expirement where a raw egg was spun and then stopped. After being stopped, it went back to spinning...

Homework Statement A rod attached to a ceiling at one end and a disc on the other end is performing SHM. In case (1) the disc cannot rotate. In case (2) the disc can rotate about its centre. Compare the restoring torque and angular frequency in both cases. Homework Equations...

Hi all, You can use superposition to add moments of inertia when they're calculated about the same center of gravity (cg), but let's say you calculate the moments of inertia of several elements of a system about one cg and then use the Parallel Axis Theorem to then reference the total moments...

Homework Statement Two blocks m (16kg) and M (88kg) are as shown in the figure. If the co-efficient of friction b/w the blocks is 0.38 but the surface beneath the block is frictionless, what is the minimum force required to hold m against M? Homework Equations Fnet = ma Fs = μs*Fa The...

Homework Statement how far from the rim of a disk of Radius R must the pivot point be located in order for its period of oscillation to be a minmum where R is the distance from the point to the centre of mass? I'm stuck at the derivative because I saw a similar problem where the answer is...

Homework Statement A crucial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R0 and mass M. It then has a circular hole of radius R1 drilled into it. The hole's center is a distance h from the center of the disk. Find the moment of inertia of this disk (with...

Homework Statement This is not a specific problem, I was just wondering, what unbalanced force acts on your body when you are in a car traveling at a constant velocity and the car comes to a sudden stop? This has to do with Newton's First Law, but I'm unsure of what force applied to your body...