Moment of inertia Definition and 1000 Threads

Hey everyone, Im solving a group of questions based on a system of particles, A(2,0) with a mass of 4kg, B(0,1) with a mass of 6kg and C(1,1 ) with a mass of 3kg. I have to find the centre of mass and also calculate the moment of inertia. To find the centre of mass I am attempting the...

Homework Statement When we put together 4 rod in case they will construct a square and when we hang it from the corner. How can we find its total moment of inertia? Length of rods: L Mass of rods: M Homework Equations Paralel Axis Theorem: I = I + Md^2 The Attempt at a...

How would one calculate the moment of inertia of a solid sphere (of uniform density, rotating about the axis through its center)? I know it's 2MR^{2}/5 but I got 3MR^{2}/5 when I attempted to derive it (just for fun, because I find rotational dynamics rather interesting). I would prefer a...

This is not homework, just my practise question for an exam. I keep getting an answer of 3/5MR^2 when the correct one is 2/5MR^2, and that was only because I fluked it by deciding to change my intergrand a little bit. I've some sources including one from hyperphysics which suggests...

a uniform solid block has mass 0.172 kg and edge lengths a=3.5cm, b=8.4cm, and c=1.4cm (c is the height of the rectangular solid).Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. i know the formula is integral of r^2 dm, but i have no...

1. Derive the moment of inertia of a sphere with thick walls.Homework Equations I=(.5)(M)(R^2+R^2) ? one is for the inner radius the other is for the outer radius. The Attempt at a Solution I believe this can be found by integrating a series of infinitely thin cylinders with different size...

I have built a model of rotating blades of a helicopter and want to mathematically calculate it's moment of inertia. I am unsure on how to do that. Its a simple model: a square wooden base with uniform thickness and 4 equally long blades made of styrofoam from the midpoints of the 4 sides of the...

Is there a reason the moment of inertia is called the "moment" of inertia? A while back, for whatever reason, I remembered how the moment of inertia is formulated and I realized it had similarities to the e/m moments; that is the integration of the mass density multiplied by coordinates. In...

Homework Statement A gyroscope consists of a solid disk of diameter 1m and mass 100kg mounted on an axis passing through the center of mass of the disk. (a) Calculate the moment of inertia of the disk about its rotational axis. (b) What is the kinetic energy of rotation of the disk if its...

h have a T shaped object (2-d) for which i need to find the moment of enertia, i used a parallel axis theorem, then to check myself i found i site which had a direct equation for it http://www.efunda.com/designstandards/beams/SquareTbeam.cfm what i did b1=100mm h1=12mm b2=12mm h2=75mm...

h have a T shaped object (2-d) for which i need to find the moment of enertia, i used a parallel axis theorem, then to check myself i found i site which had a direct equation for it http://www.efunda.com/designstandards/beams/SquareTbeam.cfm what i did b1=100mm h1=12mm b2=12mm h2=75mm...

Hi PFians What is the significance of area moment of inertia and second moment of inertia? Well, I know that it signifies resistance to bending but how can you explain practically. I mean if we see mass moment of inertia, we can say that it tells us how mass is distributed in 3d about an axis...

Homework Statement A) a horizontal disc of diameter 12.0cm is spinning freely about a vertical axis through its centre at an angular speed of 72 revolutions per minute. a piece of putty of mass 5.0g drops onto and sticks to the disc at a distance of 4.0cm from the centre. The angular speed...

A uniform sphere is rolling without slipping on a horizontal surface at 2m/s. It then rolls without slipping up a hill to height h, where it briefly comnes to rest. Find the vertical height h. [The moment of inertia, I, of a sphere is 2/5 mR^2] where m is the mass and R is the radius of the...

Here is the problem I am working on. Here is the work I have so far, does this look right. A grinding wheel that has a mass of 65.0 kg and a radius of 0.500 m is rotating at 75.0 rad/s. (The carousel can be modeled as a disk and assume it rotates without friction on its axis) a) What is...

Homework Statement A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is the rotational inertia (moment of inertia) of the sphere about an axis passing through its center? Homework Equations The Attempt at a Solution I = 2/3 MR^2 for a...

1. Find the Moment of Inertia of a Quarter Disc which has mass M and radius R about the axis passing through the center (of original disc) and perpendicular to the plane. 2. The attempt at a solution I found the Moment of Inertia (I) of a disc about the axis passing through the center...

Homework Statement The work done in accelerating a flywheel from rest to an angular speed of 14.5 revolutions per second is 22.0 kJ. What is the moment of inertia of the flywheel?Homework Equations ½Iω² = 22.0 kJThe Attempt at a Solution ½Iω² = 22.0 kJ I = (2)(22.0 kJ)/ω² ω = (14.5 revs/sec) =...

Homework Statement A skater spins with an angular speed of 8.3 rad/s with her arms outstretched. She lowers her arms, decreasing her moment of inertia by a factor of 8.9. Ignoring the friction on the skates, determine the percent of change in her kinetic energy. Answer in percent...

Homework Statement The density of Earth, at any distance r from it's center is approximately p(r) = [14.2 - 11.6 (r/R)] * 10^3 kg*m^-3 where R is the radius of the Earth. Show that the density leads to a moment of inertia I = 0.330 MR^2 about an axis through the center, where M is the...

Homework Statement The combination of an applied force and a frictional force produces a constant total torque of 39.9Nm on a wheel rotating about a fixed axis. The applied force acts for 4.5s, during which time the angular speed of the wheel increases from 3 rad/s to 12 rad/s. The applied...

Homework Statement A 16 g CD with a radius of 6.0 cm rotates with an angular speed of 42 rad/s. (a) What is its kinetic energy? Homework Equations k=1/2Iw^2 The Attempt at a Solution k=1/2(0.016x0.0036)(1764)=0.05 J

Homework Statement There are two blocks, one of mass m1 and the other of m2. They are connected by a rope that runs over a pully of radius R and interia I. m2 slides down a frictionless incline at an angle theta, and m1 hangs virtically while being pulled up by the tension in the rope. Find...

Homework Statement a) A disk with radius R and mass M is rolling without slipping on a level surface, as shown. The moment of inertia about an axis perpendicular to the page and through the center of the disk is I. If the center of the disk is moving at speed v, what is the kinetic...

Homework Statement a) Four point particles, each of mass m, are arranged in a square and attached by massless rods that run along the sides of the square, and along the diagonals. The length of each side of the square is a. The construction is then pivoted about an axis perpendicular to...

Homework Statement Using masses, springs a stop watch and ruler, determine the location of the center of mass and mass moment of inertia about an axis passing through the center of mass of a bicycle crank. The Attempt at a Solution I've been staring at this problem for a while now...

Here is the picture of the problem: http://yfrog.com/3uwtfup I understand every other step except for the equation for moment of inertia. In my book the most basic equation for moment is ΔI = (r)^2 Δm but for this problem ΔI = (1/2)(r)^2 Δm. Why is that? Does it have something to do with the...

Homework Statement Figure (a) shows a disk that can rotate about an axis at a radial distance h from the center of the disk. Figure (b) gives the rotational inertia I of the disk about the axis as a function of that distance h, from the center out to the edge of the disk. The scale on the I...

I have this situation here: I'm given the masses for the objects, as well as the radius and mass of the pulley. I have to use conservation of energy laws to find out how fast the mass on the right is going the instant it hits the ground. I can find out what the alpha of the pulley is...

A solid sphere w/ mass 100kg and radius 1m is spinning on axle. A brake pad is used to slow it down to a stop. While braking a force of 1N is applied on the pad. The coeff. of friction b/t pad and sphere is 0.5. The sphere is initially spinning at 100 rev/s, how long will it take to stop...

Hi guys Can anyone explain what is physical significance polar moment of inertia. Well i know it's formula e.g in case of shafts but not it's physical meaning.

Homework Statement Let \Omega represent a two dimensional material region who density is given by \rho(x,y). Establish an integral formula for the moment of inertia of the material region about the line y=x. Homework Equations The moment of inertia about the x axis...

Homework Statement What is the moment of inertia about the y-axis for the system as shown. The stick has a length of 2L and a mass of M. The solid sphere has a diameter of L and a mass of 2M. Homework Equations I=\intr2dm \lambda=\frac{m}{l} The Attempt at a Solution Should...

Moment of Inertia A particle of mass 0.400 kg is attached to the 100-cm mark of a meter stick of mass 0.100 kg. The meter stick rotates on a horizontal, frictionless table with an angular speed of 4.00 rad/s. Calculate the angular momentum of the system when the stick is pivoted about an axis...

please help me to understand moment of inertia

Homework Statement A lawn sprinkler has three spouts that spray water, each r = 15.5 cm long. As the water is sprayed, the sprinkler turns around in a circle. The sprinkler has a total moment of inertia of 9.10 10^-2 kg · m2. If the sprinkler starts from rest and takes 2.60 s to reach its...

I'm looking at some wheel/tire combinations for auto racing, and trying to decide which combination would out-accelerate or have more grip cornering. combo 1: 225/45r15 tire on 15"x8" wheel; 34.2 lbs total weight; diameter 23.0" combo 2: 195/50r15 tire on 15"x7" wheel; 28.4 lbs total weight...

Homework Statement A string is wrapped around a uniform disk of mass M = 2.5 kg and radius R = 0.04 m. Attached to the disk are four low-mass rods of radius b = 0.09 m, each with a small mass m = 0.6 kg at the end in an "x" configuration through the center of the disc. What is the moment of...

Hi guys, I would like to derive the Ixy equation from simple integration and I can't seem to get the right answer (third equation down the picture). I seem to be able to derive Ixx and Iyy easily but product moment of area requires first moment of area to be calculated and I just don't know...

Hi, i am trying to find the moment of inertia of a uniform density solid sphere about z-axis I = integrate => x^2 dm x = perpendicular distance from z-axis to anywhere in sphere so by pythagorus theorem, r^2 - z^2 = x^2 since dm = p dV and V = 4/3 (//pi)r^3 dV = 4(//pi)r^2 dr so I =...

Homework Statement Use integration to determine the moment of inertia of a right circular homogeneous solid cone of height H, base radius R, and mass density \rho about its symmetry axis Homework Equations Volume of cone = 1/3*pi*r^2*h I = \int r^2 dm \rho = m/v The Attempt at a...

Homework Statement The polar ice caps contain about 2.3*10^19 kg of ice. This mass contributes essentially nothing to the moment of inertia of Earth because it is located at the poles, close to the axis of rotation. Because of Global warming, all the ice has melted and formed a uniform coat of...

Homework Statement Four sheets are displaced by d from the center and they are equal and have w by h dimensions with a mass m. It is required to find the moment of inertia around the axes x and z as shown in the figure attached. Homework Equations I=(mh^2/3)+(mw^2/12) The Attempt at...

Homework Statement specific volume of steel = 489 lb/ft^3 http://ultraxs.com/image-5D1E_4AFD177E.jpg Homework Equations I tried using Ixo=1/4mr2+1/12ml2+md2 The Attempt at a Solution I tried using d=70mm because of the parallel axis therm, but that was wrong. my... r=110mm...

Homework Statement A uniform bas has two small balls glued to its end, the bar is 2.00 m long, and it has a mass 4.00 Kg, while the balls, have mass 0.500Kg and can be treated as point masses. Find the moment of inertia of this combination about each of the following axes. a) an axis...

I'm attempting to derive the moment of inertia for a cylindrical object. I know that I=\int r^2 dm which equals =\int r^2 p dV My question begins here, the derivations I seen pull p out of the integral, which makes sense to do, because in this case it's a constant. p=M/(\pir^2L). So if I...

Homework Statement A thin uniform wire is bent into a rectangle. The short, vertical sides are of length a, and the long, horizontal sides are of length b. If the total mass is 31.00 grams, a = 25.00 cm and b = 44.30 cm, what is the moment of rotational inertia about an axis through one of the...

First, this is not a homework assignment even though it may seem like a homework type question. I have no problem with the derivation of the moment of inertia of a cylinder but am having more trouble with a sphere. I completely understand the often referenced disk method, but, I would like to...

Homework Statement A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b. Express your answer in...

pulley, blocks, moment of inertia... :S Two blocks are connected by a light string passing over a pulley of radius 0.20m and moment of inertia I. The blocks move (towards the right) with an acceleration of 1.00m/s^2 along their frictionless inclines . Mass A is on an incline of 32 degrees...