Moment of inertia Definition and 1000 Threads

for "r" in mr^2 is it the shortest distance? (consider a square with point mass at the corners connected by rods, r is closer if you take the diagonal height rather than the rod distance.)

A physics student measures the period of a physical pendulum about one pivot point to be T. Then he finds another pivot point on the opposite side of the center of mass that gives the same period. The two points are separated by a distance L. Can he find the acceleration due to gravity, g...

A rod has mass M and length L. Calculate the moment of inertia of the rod about an axis which is passing through its center of mass and forming an angle \theta to the rod. I drew a diagram on an xy-plane where the rod is on the x-axis and the center of the rod is at the origin. Chopping the rod...

Homework Statement I need to derive an expression for the moment of inertia of the two masses at the ends of the arms of a speed governor Homework Equations The Attempt at a Solution The equation for the moment of inertia of a system of particles rotating about a given axis is...

I have been deriving the moment of inertia of a solid cylinder and have got this far: I=∫ r2 dm and dm=dv *density h=height r=radius \rho=density To get to the correct I=1/2mr2. you need to make dv=2\pirh dr why isn't it dv= dv=\pir2h as in volume=cross-sectional area*height

The question says: Imagine a solid disk, made of uniform material, a radius R and thickness L. What is the ratio of L/R if the moment of inertia of this disk about the axis passing through the center and perpendicular to the plane of the disk is the same as the moment of inertia about the axis...

Homework Statement [PLAIN]http://img59.imageshack.us/img59/9484/fp5.gif to find the moment of inertia through point A Homework Equations I = \int{r^2dm}The Attempt at a Solution Used a double integral from point A: \displaystyle\int_{0}^{h}\displaystyle\int_{-L/2}^{L/2}\rho(x^2+y^2)dxdy =...

Homework Statement A cone with height h and radius R. The radius R is located at the top of the cone. We have to find moment of inertia of the cone. The disc has a radius r, height of dz, and is located z below the circular surface with radius R. Homework Equations dI = \frac{1}{2}\ dm\ r^2...

Homework Statement A pendulum constructed of a solid sphere, bar, and block, each with mass m=4 kg The sphere has radius R, The bar attaches the block and sphere and has length 2R, and the block has a center of mass R away from the end of the bar. The axis of rotation is halfway between the...

Homework Statement Four point masses are arranged on the xy plane as follows. Mass1 = 27.0 grams at x = 2.00 cm and y = 2.00 cm. Mass2 = 31.0 grams at x = 0.00 cm and y = 4.00 cm. Mass3 = 49.0 grams at x = -3.00 cm and y = -3.00 cm. Mass4 = 31.0 grams at x = -1.00 cm and y = 2.00...

I would like to know the formula for Moment of inertia for horizontal rotation of circular tube(i.e wheel) of mass 65kg, wheel dia=2m, tube dia=0.1m.

Homework Statement A student hold a 2.0 kg textbook to their chest as they spin at an angular velocity of 6 rad/sec. Assuming the mass moment of inertia of the student to be 1.4 kgm^2, what is the angular velocity if the student hold the book 0.7 meters awayHomework Equations The Attempt at a...

Homework Statement If two objects have the same moment of inertia, they must have the same mass. The Attempt at a Solution I think it's false but I can't figure out why.

Homework Statement What is the moment of inertia of a solid cylinder (of mass 8.41kg and radius 7.5cm) rotating about an axis parallel to the symmetry axis but passing through the edge of the cylinder?Homework Equations I=.5mr2, but how does this change when the axis is passing through the edge...

Homework Statement A uniform circular turntable of mass 2m and radius R is at rest in space. Koko throws a lump of putty of mass m and speed v toward the edge of the turntable so that it sticks at the extreme edge of the turntable at R. Using conservation of L, show that the angular...

Homework Statement We recently had a Physics lab where we were expected to find a relationship between the moment of inertia and discs of varying radius (discs have same mass), and develop a general equation to illustrate the relationship between moment of inertia and radius for discs of any...

Homework Statement Consider a rigid rod-plus-disc system Find the moment of inertia of the pendulum as it freely rotates about the point P. The rod has a length 0.62 m, and the disc has a radius half that. The pivot at P is a fourth of the way from the end of the rod. The rod has a mass of...

Homework Statement A grinding wheel is initially at rest. A constant external torque of 52.5 N· m is applied to the wheel for 18.4 s, giving the wheel an angular speed of 605 rev/min. The external torque is then removed, and the wheel comes to rest 101 s later. Find the moment of inertia of...

Homework Statement A metal sign for a car dealership is a thin, uniform right triangle with base length b and height h. The sign has mass m. What is the moment of inertia of the sign for rotation about the side of length h? Homework Equations I = \intr^{2}dm The Attempt...

Homework Statement An object is formed by attaching a uniform, thin rod with a mass of mr = 6.94 kg and length L = 5.56 m to a uniform sphere with mass ms = 34.7 kg and radius R = 1.39 m. Note ms = 5mr and L = 4R. What is the moment of inertia of the object about an axis at the right edge...

Moment of Inertia of an object rotating about its center of mass?? Homework Statement An object is formed by attaching a uniform, thin rod with a mass of m = 6 kg and length L = 4 m to a uniform sphere with mass M = 30 kg and radius R = 1 m. What is the moment of inertia of the object about...

Homework Statement Today I had a physics lab. It involved a hanging mass on a string that hung off the table. It went through a pulley and the string was then spooled around a rotating spool on the table. We first measure the radius of the spool. Then we figured out the mass it took to...

How to Calculate Moment of Inertia for a flat rectangular plate of length 'l' & width 'w' with axis of rotation along the width 'w' (the axis of rotation is parrallel to edge of width)

Hi guys, just wanted to know how the moment of inertia of a turbine-compressor spool can be calculated. How about starting with the units as stacks of discs of reducing diameter to the fore. And also has anyone any idea of the minimum speed (torque) of a GT4088 turbocharger. I couldn't find it...

Homework Statement Moment of inertia of spherical shell of radius R, mass M along its rotation axis is given by \frac{2}{3}MR^{2} I am trying to calculate thisHomework Equations The Attempt at a Solution This is my attempt but is unsuccessful, since the spherical shell is an assembly of rings...

Homework Statement What is the moment of inertia of the plate about z axis? Homework Equations The Attempt at a Solution Consider the isosceles triangle to be a part of a square of side l/root(2) Its mass will be 2M We know that its moment of inertia about the centre...

Homework Statement HI Can anyone help me in finding out the polar moment of inertia of a hollow shaft with 3 circular slots . Its used in design of DIVERTERS in oil and gas application. Homework Equations The Attempt at a Solution

Homework Statement A regular square pyramid (base length a, height b) is spun about its axis of symmetry z. Calculate its moment of inertia about the z axis Homework Equations volume of pyramid centre of mass The Attempt at a Solution have found volume and centre of mass. I know...

Homework Statement Am I going about this the right way? There is a sphere of radius 3 and a region that lies between the planes z=1 and z=2 and has a density of cz. We are asked to work in cylindrical coordinates.Homework Equations Let \rho=\sqrt{9-z^2}, is the following the right formula...

Hi If the moment of inertia exist to resist a body to change from its rotational motion and linear inertia exists to resist a body's change from its linear motion, then for a point mass on a rotating body, which inertia does it obey? Thanks.

Homework Statement What is: Moment of inertia of two solid spheres, radii each r[0], attached by massless rod which is also of length r[0], so that the distance between the two solid spheres' centres is "3*r[0]"? The axis of rotation could either be 1) through both spheres and along the...

why is moment of inertia varyiing with the square of the radius?? hello, where ever i search moment of inertia on the web or on textbooks ,it starts with a definition saying that it is the product of mass the square of the radius. my question is why is moment of inertia defined like mass...

Hey guys, I have this really annoying last question on my assignment which is a pain. It combines 3 physics principles together. I am having problems specifically with 2) 3) and 4) 2)I know that T = | r x F |, but what kind of general vector do I use to represent F? 4) I have no...

can an object be released in space where there is no friction, to travel with a constant velocity as an force will always produce an acceleration. as moment of inertia says if an object is flying with an velocity say 20m/s, it will continue to do so unless external force is applied.

Homework Statement This is the cross sectional are of the shape: http://img38.imageshack.us/i/shapep.jpg/" It's made of 2 10"x1" plates. (Picture is not to scale) Q (first moment of inertia) above and below the neutral axis should be the same. For some reasons, my calculated Q above is...

Hi Thinking about a simple stable wheel at rest on a flat surface with a force applied at the axle parallel to the ground trying to work out the resultant translational force (note: no slipping, static friction is very high, no rolling resistance) I think it is the ratio between the...

Hi Folks, I am designing a piece of kinetic scultpure that will involve cubes made from aluminium square tubing rotating around an axis that passes through two diagonal corners. I am trying to determine motor size to drive this thing, and to do that I need to know its moment of inertia. Math...

I'm working on a project to replace hollow structures, (pipe, sq. tube, ect...) with open structures, (channels, angle iron, ect...). It's been a while and I think that all I would have to do is compair the moment of inertia for each of these shapes and make sure that they match or are larger...

I was looking at the moment of inertia list that they have on Wikipedia and noticed that the moment of inertia for a regular polygon was rather complicated. I did the calculation myself and found a significantly simpler result of I = (m/6)(3+tan(pi/n)^2)*R^2: m is the mass of the...

so i have to find the moment of inertia of a solid cone given by the equations z = ar and z = b by using a triple integral. The density of the cone is assumed to be 1. so the integral looks like ∫ ∫ ∫ r^2 dV. so first i did it with dV = rdrdθdz with limits r (from 0 to z/a), θ (from 0 to 2pi)...

Perhaps Tensor Calculus holds the answer; but I just can't justify the time for studying that as I know nothing of it. The end objective is to calculate the mass moment of inertia of the yellow solid parallelepiped about rectangular axes through its centre of mass as in the diagram here...

Homework Statement A uniform circular disk has radius 36 cm and mass 350 g and its center is at the origin. Then a circular hole of radius 7.2 cm is cut out of it. The center of the hole is a distance 10.8 cm from the center of the disk. Find the moment of inertia of the modified disk about...

A stick of uniform density with mass M = 7.5 kg and length L = 1 m is pivoted about an axle which is perpendicular to its length and located 0.12 m from one end. Ignore any friction between the stick and the axle. a) What is the moment of inertia of the stick about this axle? Iaxle = kg...

Hi, An old GRE problem asks what the moment of inertia of seven pennies, arranged in a hexagon with one in the center, all touching each others' edges is, about the axis that passes through the center of the central penny and is normal to the plane of the pennies. Each penny is a uniform...

Homework Statement Derive an expression for the moment of inertia about the axis of symmetry for a cylinder of mass M , length L and radius a, where the mass density decreases as a function of distance from the axis as 1/r Homework Equations The Attempt at a Solution 1) am i...

Homework Statement For a little background, this lab was on energy of a rolling object. We rolled a hollow cylinder from the top of a ramp on a table and onto the floor. We are trying to experimentally derive the constant (k) found in the equation for moment of inertia. Variables: h =...

Homework Statement 2 children, masses 35kg and 40kg sit at opposite ends of a 3.4m seesaw with mass 25kg with the fulcrum at midpoint. with the seesaw horizontal find a) the net torque b)angular acceleration Homework Equations tau=rF=Ialpha The Attempt at a Solution i got the right...

Help: Moment of inertia Ixx, Iyy, Izz, Ixy, Ixz, Iyz, etc?? Hi all, Can someone help with a few equations?, i need to know the moment of inertia of a section. The section is a column which in the Z direction have 3m, on the X direction has 0.3m and on the Y direction has 0.6m. I know...

Homework Statement see attachment Homework Equations The Attempt at a Solution Hey can someone please tell me what I've done wrong here. There is all so a question further down that asks for the same thing but with mass of the bar included.(M_bar)

Homework Statement Consider a particle of mass = 19.0 revolving around an axis with angular speed . The perpendicular distance from the particle to the axis is = 0.500 . Homework Equations I=mr^2 K=0.5Iw^2 The Attempt at a Solution I=4.75 K=1796 which is 0.5*4.75*27.5^2...