Moment of inertia Definition and 1000 Threads

what is the moment of inertia about the wheels , when the vehicle is accelerated upto 100 km/hr and the foot is lifted off the accelerator

Homework Statement In the image attached, I'm asked to find the mass moment of inertia about an axis at point O that's perpendicular to the page. The Attempt at a Solution The only question about this problem that I have is: Can I divide the composite body at point O and find the...

Homework Statement A drink can is placed on a rough-surfaced, stationary conveyor belt of a supermarket checkout. The can is modeled as a cylinder consisting of two equal discs, each of mass m1 and radius R, that are the top and bottom, and a curved surface of mass m2, radius R and length h...

Homework Statement A person grabs on to an already spinning merry-go-round. The person is initially at rest and has a mass of 29.5 kg. They grab and cling to a bar that is 1.70 m from the center of the merry-go-round, causing the angular velocity of the merry-go-round to abruptly drop from...

Homework Statement A uniform thin rod with mass 4.59 kilograms pivots about an axis through its center and perpendicular to its length. Two small bodies with a mass of 0.543 kilograms, are attached to the ends of the rod. What is the length of the rod such that the moment of inertia of the...

for part a I used the equation I=m*r^2 ---> 120(58/100)^2=40.36 kg*m^2 b)I know how to do this using the equation K=1/2Iw^2 but my moment of inertia is incorrect.

Homework Statement Water falls onto a water wheel causing it to rotate. Consider an instant when the water wheel is initially motionless and then 100 kg of water hits tangent to the wheel at a radius of 2 m (this water can be treated like a point mass). If the moment of inertia of the water...

In the figure, two skaters, each of mass 48.1 kg, approach each other along parallel paths separated by 2.90 m. They have opposite velocities of 1.61 m/s each. One skater carries one end of a long pole of negligible mass, and the other skater grabs the other end as she passes. The skaters then...

Homework Statement The thin rod shown has a length L = 100 cm, and a density that varies from 26 g/cm at the origin to 3 g/cm at the far end. Determine a) the moment of inertia about axis 1 (passing through the center of mass of the rod), and b) the moment of inertia about axis 2 (passing...

Homework Statement A compound disk of outside diameter 152 cm is made up of a uniform solid disk of radius 41.0 cm and area density 3.30 g/cm2 surrounded by a concentric ring of inner radius 41.0 cm , outer radius 76.0 cm , and area density 2.10 g/cm2 . Find the moment of inertia of this...

Homework Statement A thin walled hollow sphere of radius 16 cm is sliced in half. What is the moment of inertia of this hollow hemisphere about the x-axis if the areal density is 90 g/cm2? Homework Equations No idea The Attempt at a Solution I've had no luck with this. I've...

Homework Statement Two uniform square laminas are combined into a single body. One lamina ABCD has mass 5m and the other lamina PQRS has mass m. The lamina PQRS has side 2a, and its vertices are at the mid-points of the sides of ABCD, with P on AB and S on AD. The line PS meets AC at K, and...

Homework Statement Can i use "pyramid" method to derive the equation of Moment Inertia solid sphere? The pyramid is such we slice a watermelon. Sorry for my bad english. Regards. Homework Equations 2/5 MR^2 The Attempt at a Solution

Homework Statement You guys might recognize me from a post earlier. Yep, I'm still plugging away at rotation of rigid bodies and have another question. The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rpm to 520...

Homework Statement A molecule similar to methanol is made by joining three flourine atoms (purple; m = 19 amu each) to one carbon atom (blue; 12 amu) to one oxygen atom (green; 16 amu) to one potassium atom (orange; 39 amu). The position of each atom is as follows: 1. The flourine atoms...

Homework Statement If the fall height of the mass is doubled, the angular acceleration of the wheel will a. decrease by an unkown amount b. remain unchanged c. decrease by a factor of 2 d. increase by an unknown amount e. increase by a factor of 2 Homework Equations The...

Homework Statement 25-2-EX9 The time rate of change of the displacement (velocity) of a robot arm is ds/dt = 8t/(t^2 + 4)^2. Find the expression for the displacement as a function of time if s = -1 m when t = 0 s. 26-5-9 Find the moment of inertia of a plate covering the first-quadrant region...

[b]1. Homework Statement [ How do I get I1( the moment of inertia of the picture b) ?is just a math problem but really no idea. Homework Equations I=mr^2 The Attempt at a Solution maybe centre of mass . Guide will do . please help , thank

Homework Statement An object is formed by attaching a uniform, thin rod with a mass of mr = 6.91 kg and length L = 4.88 m to a uniform sphere with mass ms = 34.55 kg and radius R = 1.22 m. Note ms = 5mr and L = 4R. What is the moment of inertia of the object about an axis at the left end...

[b]1. The

Hi Guys, I am trying to calculate a starting torque required to move the drum at 6rpm that weights 2000kg and has 1200mm in diameter. There would be no problem to do this calc in normal circumstances as I can find a moment of inertia formula for a pipe in my book. But in this case there...

Homework Statement Starting from the sum: I=Ʃ mα*ρα2 and replacing it by the appropriate integral, find the moment of inertia of a uniform thin square with side length 2*b, lying in the x-y plane, rotated about the x-axis. Calculate its moment of inertia. Homework Equations The integral form...

Homework Statement Derive the formula for rod's moment of inertia: I = ml2/12 Homework Equations I = ml2/12 The Attempt at a Solution The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some...

Homework Statement Hi there. Im trying to find the moment of inertia for a 2/3 empty cylinder, could anyone see if I solved this correctly? Someone told me it's wrong, but I don't know why exactly, so any thoughts would be much appreciated. (I added the question and the attempt to solve it in...

Homework Statement I have a physical pendulum that is rotating about an fixed axis. The period is: T=2\pi \sqrt{\frac{I}{mgd}} I = moment of inertia d = distance between the center of mass and the axis. The problem is: If you add a mass in the end of the pendulum. The period is going...

Hi, Homework Statement Will the moment of inertia of a two dimensional rectangle (with sides a, b) whose axis is parallel to one of its sides and passes through its center of mass, be (1/12)M(a2+b2)? Homework Equations The Attempt at a Solution

Homework Statement Four particles with masses 2 kg (top left corner), 3 kg (bottom left corner), 4 kg (bottom right corner), and 5 kg (top right corner) are connected by rigid rods of negligible mass. The origin is centered on the center of the rectangle of sides 0.8 length and 0.6 breadth. If...

Homework Statement The question is from a lab. The lab used an Atwood Machine with two masses suspended string looped over a pulley. The time for one mass to reach the ground was measured and acceleration of the mass was calculated. The results were plotted on a graph of weight difference...

Homework Statement Hiya boys, Sorry i don't know how to proceed with this problem can anyone help me solve these two questions? In preparation for building a space station, an astronaut removes a self-telescoping uniform rod from the cargo bay and releases it, not noticing that he gave...

Homework Statement Find the second moment of inertia of a rectangle. The Attempt at a Solution Anyone know why my answer is 4 times too big?

Homework Statement Hi, I have been asked to find the moment of inertia of a rolling ball. The ball can be any size and radius. I have chosen a solid ball. The experiment says that I should roll the ball down a ramp and then measure the time it takes for the ball to roll from the end of...

I am having trouble right now with the same problem (finding Ixx and Iyy). \begin{equation} I_{yy} = \int(x^2 + z^2)dm \end{equation} where \begin{equation} dm = \frac{2M}{R^2 + H^2} q dq \end{equation} and q is my generalized coordinate that is measured from the origin down the length of the...

KErotational = (1/2)Iω2 420 = (1/2)Iω2 420 = (1/2)I(402) 420/(402) = (1/2)I 0.2625 = (1/2)I 2(0.2625) = I 0.525 = I 0.53 = I

Homework Statement Hey In my assignment I am writing about beamdeflection, but there's some things i really can find out how to do. I need to explain area moment, moment of inertia and the center of gravity, i need to explain this with the help of integration. Under her I've inertet...

Hello everyone, (This might be a little long winded but I would very much appreciate some help on this!) Today while in psychology class, I was thinking about a much more important subject, namely a project I want to start working on. Basically what I want to do is build a motor from the...

Homework Statement Find the moment of inertia and center of mass of: A uniform cone of mass M, height h, and base radius R, spinning about its symmetry (x) axis. Homework Equations I = ∫R^2dm The Attempt at a Solution I tried using I =∫R^2dm, solving for dm I got dm=(M/V)dV...

Homework Statement [refer to picture, thanks] The "L-shaped" figure rotates on the axis which which intercepts through 9 kilogram and 2.5 kilogram masses. Find the moment of inertia of the object for this type of rotation. Disregard the masses of connecting bars. Homework Equations MR^2...

Homework Statement I was wanting to see if someone could check my calculations. I've checked out the Iy and Ix in Autodesk Inventor and what I got is wrong. Here are the links to my images. I apologize, the uploading option is not allowing me to upload the pictures...

Homework Statement An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center. The...

Homework Statement I was given a formula sheet that shows the moment of inertia equations for three shapes: rectangle, circle, and triangle. Homework Equations There seems to be two sets of MOI equations. Here are the rectangular equations: Rectanglular: Ix=\frac{bh^3}{3}...

Homework Statement Consider a solid homogeneous object taller than its wide, with the top and bottom parallel. Prove that the shape with the lowest moment of inertia about an axis through the object is a cylinder with the axis through its axis of symmetry. density, mass, and height are...

Here's a derviation from HyperPhysics: He says: dV=πy^{2}dz However, if we're finding the surface area of the sphere: dA=2πRdz≠2πydz If we cannot use dA=2πydz, how come dV=πy^{2}dz is still applicable?

Hello guys, I am calculating Bending and Shear stresses in hollow beams. We have a particular kind of shell that we use for impact loading, so we put rubber discs around the steel shell. So my question is, how will it affect the moment of inertia ? Since I know that the rubber discs will...

Homework Statement A 1.3 kg block is tied to a string that is wrapped around the rim of a pulley of radius 7.2cm. The mass of the pulley is 0.31kg. The block is released from rest. If the velocity of the block is 3.0m/s after it falls 0.5m, what is the moment of inertia for the pulley?[/b]...

Homework Statement Question is about buckling, so i know i need to work out I (moment of Inertia), which is for a hollow tube. Homework Equations So the paper states..I = (0.08^4 - 0.06^4)∏/64 = 1.37 x 10^-6 m4 When i do that on my calculator, i don't get this answer. Puzzled...

I took a picture of the question to help. I know that the moment of inertia for a rod (at one end, not the center) is: 1/3ML^2 And I know that the period of oscillation is: T=2∏√(L/g) But I don't know how to relate them... I tried doing Torque=Iα=Fdcosθ and solve in terms of...

Hello everyone! Here is the link to the problem: http://i.imgur.com/2HNrQ.jpg I don't even know where to start. Any help to get started would be greatly appreciated. Thank you so much. Cheers

Can someone please explain to me what moment of inertia means?? I googled it and I found that moment of inertia is an objects resistance to angular momentum? What does that mean exactly? Can someone please briefly explain to me (in English) what it means or give me an example? Because I really...

Homework Statement This isn't homework but its part of my assignment. I am creating a center of gravity calculator for a car using excel which I can enter the locations of different components and their masses, and it will give me the center of gravity for the car. I am then using this to...

Hello everyone, I have been working on a problem and I am having a hard time figuring out if this is the right answer. Homework Statement A solid sphere of mass 10 kg and radius 10 cm is rotating about its axis. A. Find its moment of inertia B. What is the kinetic energy of the sphere if it...