Moment inertia Definition and 18 Threads

I've tried the following, but I don't get the correct result: The moment of inertia of the system with respect to the axis of rotation is: $$L=I\omega \Rightarrow I=\dfrac{L}{\omega}=\dfrac53 \, \textrm{kg m}^2$$ Then, $$I=I_1+I_2\Rightarrow I_2=I-I_1=\dfrac53 -7=-\dfrac{16}3\, \textrm{kg...

Assume the top image to be the simple version of the wheel configuration and the lower one to be the proposed way of wheel arrangement. In the newer version i want to use a heavy metal plate of approx 200gms and a wheel of 50gm instead of a heavy 200gm wheels due to sourcing issues. This is...

Hi, I’m making a vehicle simulator and I’m not entirely sure if my inertia calculations are right or are completely wrong. What I currently have now is something like this: 1. Engine: engine_Out_Inertia = engine_Inertia; this should contain the inertia of the engine and all of it’s auxiliaries...

Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex. Can I split the rotated square to two squares in the x-z plane and y-z plane to find...

On speeding up: τload - τfriction = Iαup On speeding down: τfriction = Iαdown If i substitute τfriction from speeding down to speeding up equation, i get moment of inertia: I = (τload)/(αup+αdown) But, is this allowed? Does friction torque in speeding up is equal to friction torque in...

Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure. Find the maximum velocity the ring must roll so that it doesn't...

Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the...

Suppose i have an equilateral triangle and i want to find the principal axes of rotation passing through one of the vertex. How can i do that? I am thinking along the following lines but I'm not too sure: 1)Since the equilateral triangle has symmetry about a median, that definitely is one...

Homework Statement A 45 RPM record is a disk with a wide hole in the center. The mass of such record is 45g. It is 7 inches in diameter, and the hole in the center has a 1.5 inch diameter. (Sorry for the odd units, this was the way it was given). Find the moment of inertia of the 45 RPM...

I need to make a project that integrates physics with math, involving the use of integrals to find moment inertia of areas. The theory could be read here :http://www.intmath.com/applications-integration/6-moments-inertia.php I need to make an object that applies the theory above. Can anybody...

Moment inertia -- theoretical problem Homework Statement Show that the moment inertia of a hollow cylinder with inner radius a and outer radius b is (1/2)*M*(a^2+b^2), calculated for the center axis. Homework Equations I know that the moment inertia of a non-hollow cylinder is I =...

Homework Statement Calculate the moment of inertia of a uniform rigid rod of length L and mass M lying along the x-axis which rotates about an axis perpendicular to the rod (the y axis) and passing through it’s center of mass. The rod has a line density that is a function of location such...

Hey y'all, A plea for general advice here as I embark on a project. Say I have an object rotating around an axis but *displaced* some distance "r" from that axis. It's length, a dimension perpendicular to the axis, is "a." I'm interested in finding the mass moment of inertia for the object...

To which of the two cubes has a larger moment of inertia? I think it's the right one because We know that the minimal moment of inertia is throw the principal axes that goes throw the center of mass. in the right one , the rotation isn't throw the principal axes . there is also the following...

Hi.. I've got a problem about moment inertia. I don't understand about looking the distance of centroid (y). I am still confucing about the formula of "y" in Moment Inertia. Can you shows me about the formula of y or if any thread for this before, I am glad to see it too.Thanx's for your help...

How do I derive the formula 1/12 Ml^2? Derive the formula for moment of inertia of a uniform thin rod of length l about an axis through its center perpendicular to the rod.

Hi Ho! I know that many books show the way to derive the moment inertia of a solid and a hollow sphere in many ways, each according to the lines of reasoning of their authors. I also have my own line of reasoning that I have successfully applied in finding the moment inertia of a solid...

what is the difference between moment of inertia and moment inertia tensor?