Moment of inertia Definition and 1000 Threads

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...

suppose a platform "P" is rotating about the z-axis wrt x-axis . another platform "Q" rotating about z-axis below "P" with same angular velocity wrt x-axis standing on Q , P is at rest wrt Q, After some time rotational inertia of P about z-axis starts changing with time standing on Q , P will...

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 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...

1. Homework Statement A cylinder of mass M and radius R rolls (without slipping) down an inclined plane whose incline angle with the horizontal is theta. Determine the acceleration of the cylinder's center of mass and the minimum coefficient of friction that will allow the cylinder to roll...

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 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 Question - Models of global warming predict that large sections of the polar ice caps will melt. Explain what effect this will have on the rotation of the Earth, however slight. Homework Equations L = Iw The Attempt at a Solution Assuming polar ice caps protrude the earth...

Homework Statement I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks The Attempt at a Solution I am attempting...

in this video http://www.physicsgalaxy.com/lectures/1/44/234/Solved-Example-2#12(see only the question) the method illustrated is integration but i thought of an alternate method, moment of inertia of half disc with radius r2 is 1/2mr2^2 and that of half disc with radius r1 is 1/2mr1^2.so...

Homework Statement Theres an object which makes a pendulum motion.Lets suppose we hang the mass to the ceiling.We released the object with inital angle 0 to the ceiling.(I mean the angle between the object and the ceiling is zero).Whats the moment of the Inertia to the point A. A is a...

I'm having a hard time undertanding a concept of moment of inertia and Angular acceleration. Homework Statement We have a closed system above. M1 is a cylinder of 2 Kilograms, moment of inertia of a cylinder ( MR2 /2 ) with a string tightly rolled around it. This string connects to a free...

Homework Statement In our physics lab we were to set up a system looking like this: where the mass was released and the velocity/acceleration and of the ring was calculated using MotionLab software. Our goal was to find the predicted total moment of inertia by just calculating the moment of...

Homework Statement Find the moment of inertia of these composite objects. I've attached two different composite objects; each rod has length L and mass M. Homework Equations I = Icm + MD2 Long thin rod with rotation axis through centre: Icm = 1/12ML2 Long thin rod with rotation axis through...

Homework Statement Need to find the moment of inertia of a cylinder, about its center of mass, about the three principle axes. Z axis is normal to the circular faces of the cylinder. mass = M, radius = R, height = h Homework Equations ∑miri2 The Attempt at a Solution The Izz for whatever...

Homework Statement Find the moment of inertia for this composite object: M1=5kg at (3,4) and M2=3kg at (6,8) Homework Equations Moment if inertia for point particle = MR2 The Attempt at a Solution I'm not sure if moment of inertia should be componentized -- broken up into x and y...

This seems to be a crucial detail that I just glossed over, but when finding the inertia tensor of an object, is the origin always situated at the object centre of mass? For example: In the link (http://hepweb.ucsd.edu/ph110b/110b_notes/node26.html ), is it necessary to do the integral from...

Homework Statement The cubic is divided into 4 parts , A, B and C, D , each with thickness of 1mm , i am sked to find thesecond moment of inertia about x -axis Homework EquationsThe Attempt at a Solution i' m using the formula Ixx = Ix +A(d^2)[/B] for part CD, Ixx = 50(1^3) / 12 + 50...

I'm wondering about how one would describe the dynamics of a rotating sphere. Consider this: a solid sphere of mass "m" and radius "r" is set to rotate about a tangent to its surface. If it is released from the horizontal position such that it swings like a pendulum, what would be the force...

Homework Statement In the diagram, Disk 1 has a moment of inertia of 4.40 kg · m2 and is rotating in the counterclockwise direction with an angular speed of 7.50 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 9.50 rad/s falls...

Homework Statement What is the moment of inertia of the 4 kg disk below when it rotates about the center of mass? The mass of the disk without the holes is 6 kg . Homework Equations Center of mass equation: (1/M)(∫xdm) Moment of inertia of a disk: I = 0.5mr2 Parallel axis theorem: I = Io +...

Homework Statement The rods of length 2 meters and and mass 20 kg are joined at their ends to form a V shape. What is the total moment of inertia measured from the reference point perpendicular to the plane of the paper and at the point where the two rods are joined. (So find total moment of...

For a mathematics project I'm trying to figure out the moment of inertia for a propeller. I'm told that it is possible to find the moment of inertia of irregular objects through calculus, so I'm determined to figure it out using calculus. I plan on using a 3D modelling program (since I don't...

Homework Statement An object rolls down a ramp starting from rest, demonstrate symbolically the calculation needed to go from time given to a measured κ value here. Pick your favourite object and perform the calculation. d, m, R, t, h are known http://puu.sh/luare/10352d0479.png Soccer Ball...

Homework Statement A pendulum consists of a light rigid rod of length 250 mm, with two identical uniform solid spheres of radius of radius 50 mm attached one on either side of its lower end. Find the period of small oscillations (a) perpendicular to the line of centres and (b) along...

1. The problem statementα, all variables and given/known data The moment of inertia of a Rod over an Axis XX' passing through the center of mass of the Rod at an angle α is- Homework Equations Moment of Inertia of Rod about the end, I =ML2/3 The Attempt at a Solution I=ML2/3 Answer of the...

Homework Statement Got a spicy one for you today. There is a cylinder of mass 5kg (M) with no angular velocity and no velocity, on a surface of static friction constant μ=0.6 . It's radius is .1 meters (R). Its baricentric moment of inertia is characterized by I=.5MR^2 . Gravity is 10m/s...

Homework Statement A uniform sphere and a particle are sent one-by-one with the same initial speed up the same incline. Each rises to a maximum height before falling back towards the starting point. The sphere rolls without slipping; the particle slides without friction. Use conservation of...

Homework Statement That is the set up for experiment, and I attached the data I found in the lab. The lab given me the equation to find the moment of inertia of the cylinder Homework Equations Icyl = (2hgM_cylinder) * (1/(W_withcylinder)^2 - 1/(W_nocylinder)^2) The height is 0.9m The Attempt at...

Homework Statement To calculate the moment of inertia of a cantilevered tapered tube with mid-thickness large radius RL and mid-thickness small radius RS Homework Equations The Attempt at a Solution Area of the larger end of the tube AL=2*pi*RL*t Area of the smaller end of the tube...

Homework Statement how to divide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M. Homework Equations I=∫r2dm 2/5 MR^2 The Attempt at a Solution https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p i try to...

Homework Statement Find the moment of inertia of a spherical shell (hollow) with mass M and radius R. Homework Equations ## I = \int r^2 dm ## The Attempt at a Solution This is method I use to find Moment of Inertia of solid sphere: We use circular cross sections. At some radius r...

Homework Statement Is the moment of inertia matrix a tensor? Hint: the dyadic product of two vectors transforms according to the rule for second order tensors. I is the inertia matrix L is the angular momentum \omega is the angular velocity Homework Equations The transformation rule for a...

If a beam's y-y axis lies in the plane of the paper, do I use Ixx or Iyy from sections table?

So is a Bike driver stable when the bike is running because the bike wheels has a certain moment of inertia about the horizontal axis ,which might alter(mi gets lesser) if the direction of the axis changes ? Thanks in advance

Maximum axial load is proportional to the second moment of area. Thus can we reason that aluminium cans are cylindrical because they have a high second moment of area(mr^2) compared to other shapes(Which gives it a higher max axial load.)?

Hi, I need to calculate the moment of inertia of this flywheel so I can calculate the torque I need. T= I*alpha Attached is an image of the flywheel the cam follower that will be attached to the shaft (left shaft in this picture). When calculating the Moment of Inertia, what mass do I use...

Hi everyone, I am trying to find out the Moment of Inertia of a sphere which is all known to be 2/5(m)(r^2) I calculate this in 2 ways. One by triple integration and one by disk method. From the textbooks, moment of inertia should be in the form, dI = (r^2) dm, However, the textbook, University...

Homework Statement The diagram shows the instant when a long slender bar of mass 4.9 kg and length 4.9 m is horizontal. At this instant the mass m= 6.5 kg has a vertical velocity of 4.0 m/s. If the pulley has negligible mass and all friction effects may be ignored, what is the magnitude of the...

I am unable to find it.

Homework Statement >Problem:<br>Find the Moment of Inertia of a circular disk of uniform density about an axis which passes through the center and makes an angle of $\dfrac{\pi}{6}$ with the plane of the disc. Homework Equations Moment of Inertia ($I$) is $$\int r^2dm$$ where $r$ is the...

See image. It would be better if you can show me the calculation process. EDIT: the axis of rotation goes right through the centre of the cylinder. NEVER MIND! GOT IT!

What is the overall moment of inertia of many cylinders in contact, where each is rotated about an axis through its center of mass. For example, a set of rollers. (See picture)

I know the formula for moment of inertia is but there are I = MR^2 but there are also formulae for different objects as shown in the picture. So, how and when do you use I = MR^2 ? Just in case of (a)? Thanks!

The hoop has radius R. I used the same way to plot the axis for the hoop: ##l^2 = r^2= 4R^2cos\theta## since: ##r=2Rcos\theta## 2\rho \int_{0}^{\frac{\pi}{2}} r^2 r d\theta 2\rho \int_{0}^{\frac{\pi}{2}} 8R^3 cos^3\theta d\theta answer is \frac{32}{3}R^3\rho , and its wrong using the...

Homework Statement Given: ##\mu_B=0.52## ##\theta=30^{\circ}## Weight- ##25## lb ##\omega=0## ## l=6## ft ##r_c=3\sqrt 2## radius of curvature. Homework Equations My Equations of motion are the following: ##\xleftarrow{+}\sum F_x=N_A\sin 60 - F_B=0## ##\downarrow{+} \sum F_y= N_A \cos...

Homework Statement Given: Wheel radius is 20 CM, Gear radius is 5 CM, Coefficient of Static Friction is .2, Weight on rear wheel is 50 N. What is the minimum force that must be applied to the pedal for the wheel to begin accelerating on a level surface?Homework Equations Net T = I * a T = R X...

Looking at the image below, we have the function z^2=\frac{r^2}{a} yrevolving about y-axis. We know that y goes from 0 to "a". We also know the mass of the object (of uniform density). Do you think is my procedure correct? Do you get the same result?

Hi, I am a bit confused about the units of MI...I read that MI of rectangle is b*d^3/12,so unit is mm^4..Also i read in wiki that unit of MI is kg.mm^2... Both are correct,but why this difference is?