Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [moment-of-inertia]

The tag has no usage guidance.

-2
votes
0answers
29 views

Moment of inertia and counterweight

I need help regarding moment of inertia - i have zero clue on this topic. I have 2 sets of problems which i am told to use moment of inertia ( which i don't get it ) 1.I have to use counterweight ...
0
votes
0answers
19 views

calculate the shear stress from surface traction

The problem is that I am simulating a hollow cylinder under torsion and I would like to compute the shear stress for it. The output of the simulation is the shear surface tractions. See the figure ...
-1
votes
1answer
37 views

Moment of inertia and torque [on hold]

Why there is different moment of inertia with respect to point P about which a rigid body is moving around a circle with some velocity and spinning about its own axis compared to the one which is just ...
0
votes
0answers
40 views

The moment of inertia of a hollow sphere, except that there is a hole [closed]

The moment of inertia of a hollow sphere is $\frac{2}{3}mr^2$, where $m$ is the mass and $r$ is the radius. If a hollow sphere is rotating anticlockwise with reference to the axis of rotation at its ...
1
vote
1answer
35 views

How do you sum up torques for a macroscopic object

Torque is measured about a point. But angular momentum for some object is measured around an axis. This doesn't make sense to me as in for example, a cylinder. If there are multiple tangent forces on ...
0
votes
0answers
26 views

Physics behind finding center of mass of a stick like object [duplicate]

If I hold a rod with both hands wherever at opposite sides of the center of mass of the body, and bring them slowly close to each other, then the point my hands meet at, is approximately the center of ...
2
votes
1answer
46 views

How to calculate the inertia tensor of a spherical cap?

In this question, an attempt is made at calculating the diagonal elements of the inertia tensor of a homogeneous spherical cap, where the $z$-axis is the symmetry axis. The mass moment of inertia ...
0
votes
2answers
69 views

Angular Momentum vs Moment of Inertia

Pretty sure that this question has already been answered in this site, but I cannot find it. Anyway, here's the question: What is the difference between angular momentum and moment of inertia?
1
vote
1answer
37 views

How do I calculate the tensor of inertia of a non-rigid body?

How do I calculate the tensor of inertia of a rotating non-rigid body? Is the usual formula: $$T_{ij} = \int{\rho( x_ix_j - \delta_{ij} x^kx_k)d^3x}$$ still correct?
1
vote
3answers
139 views

Why does angular momentum being constant prove Kepler's first law?

So I was watching this video and this video on Kepler's first law in order to understand the proof of Kepler's first law. He started off by saying that for an ellipse, the distance from a focus point ...
0
votes
2answers
42 views

I am confused about which point we should take moment of inertia (moi) in diff situations

A uniform rod of mass m and length l is kept vertical with lower end clamped. It is slightly pushed to fall down under gravity. Find angular speed of rod when passing through its lowest position. I ...
1
vote
2answers
83 views

Mechanics: angular momentum of disk

I am studying mechanical engineering and I've got a problem with the angular momentum of objects that have a rotation which is rather complex to describe like the following: The shaft rotates around ...
1
vote
1answer
63 views

Can I theoretically completely convert the kinetic energy of a bullet to rotational energy of a disc, when the bullet hits it tangentially?

Will the kinetic energy of bullet be converted to rotational energy of disc(assume the bullet gets stuck to the disc). Let me assume that disc is mounted on a car standing on a frictionless surface. ...
2
votes
3answers
60 views

Where does it getting wrong , when using $v^2 - u^2 = 2as $ down the incline, for different object having different moment of inertia?

Well, Consider a situation there is a sphere and a ring, of same mass $M$ and radius $R$. They both starts rolling down the inclined plane. We know moments of them as well, $$I_\text{sphere}=\frac{2}{...
0
votes
2answers
67 views

Moment of Inertia of Infinite small rods! [closed]

Say we have a symmetrical and homogenous rod with mass $M$ and length $L$ and a rotating axis in the middle of the rod, dividing it into two halves. Its moment of inert is $$I_{cm}=\frac{M{L^2}}{12}$$ ...
2
votes
4answers
141 views

Why acceleration comes to be diffrent when using $F=ma$ and when using $\tau = I \alpha $? [closed]

Consider a Disc of mass $M$ and radius $R$, I applied force $F$ tangentially on it. Now using $F=Ma$ , acceleration comes up to $$a=F/M$$ Now, let's use the torque equation: Here, the moment of ...
1
vote
1answer
46 views

Derivation of the inertia tensor

I am trying to understand the inertia tensor of rigid bodies but I don't quite understand how it is derived. This is what I tried: Consider a rigid body consisting of $N$ point masses acted upon by ...
0
votes
1answer
63 views

Moment of inertia graph

To find the moment of inertia of an object, we take each individual mass element and multiply it by the square of its radius, and then find the sum of all these products. If the object is continuous,...
2
votes
3answers
99 views

What is $\text{kg}\cdot \text{m}^2$ concretely? (multiplication of units)

I have problem to understand what $\text{kg}\cdot \text{m}^2$ (moment of inertia) is. So, for example a force does a work of $3\text{J}=3\text{Nm}$ means that the force can displace a weight of $3\...
0
votes
2answers
26 views

Trying to get moment of inertia of a disc using moment of inertia of a rod

I know how moment of inertia of a disc is calculated using the usual way, but just for fun, I tried this way which is rather giving incorrect answer. I don't know what's the flaw in this and thus ...
0
votes
2answers
25 views

Moment of Inertia equation for small volume

Below is the equation of the moment of inertia for small volume elements, $\Delta m$ $$I = \lim_{\Delta m_i \to 0} \sum_{i} r^2_i \Delta m_i = \int r^2 dm$$ Can someone please explain it to me on ...
1
vote
1answer
32 views

Force required for Angular Accleration

Suppose I have 4' x 4' piece of wood. Its mass is 150kg evenly distributed. I drill a hole right at a corner and place rod through the hole to create a rotational axis. I apply a tangental force at ...
0
votes
1answer
19 views

What's the seconde moment of a T beam with a heel?

the seconde moment of area of a rectangle is Iy = (bh^3)/12 b : base h : height What is the second moment of area of a T beam like this one ?
1
vote
3answers
74 views

How many moment of inertia about center of mass exist?

So imagine we have a rigid body and we want to find the moment of inertia about center of mass . Doesnt exist infinite axis that pass trough center of mass therefore infinte moment of inertia? Do they ...
0
votes
1answer
54 views

Integral formula for inertia tensor

Writing down the balance of angular momentum, we introduce the inertia tensor by the formula \begin{equation} J(t)a \cdot b = \int_{S(t)} \rho (t,x)\left( a \times \left( x - X(t) \right)\right)\cdot ...
1
vote
0answers
43 views

A question on a ballet dancer and her moment of inertia? [closed]

The classical example of conservation of angular momentum. I want to ask how we know that moment of inertia around center of mass change when in same time also center of mass change position? Why ...
1
vote
0answers
181 views

Deriving moment of inertia of a solid sphere [closed]

I have been trying to calculate it on my own, but the answer I get is different to the one I can find everywhere else, so I have to be wrong. My attempt was a very straightforward one. I used ...
1
vote
2answers
130 views

How to choose the perpendicular axis?

This site https://en.wikipedia.org/wiki/Perpendicular_axis_theorem says: Define perpendicular axes $x$, $y$, and $z$ (which meet at origin $O$) so that the body lies in the $xy$-plane, and the $z$-...
-2
votes
1answer
56 views

Integration Using Spherical Coordinates [closed]

So I had to find the moment of inertia of a hollow sphere of mass $M$, radius $R$, and negligible thickness. $dI=R^2 \cdot dm$ where $dm = \dfrac{M}{4\pi R^2}\cdot R^2\sin(\theta)\cdot d\theta\cdot ...
0
votes
1answer
21 views

Is the magnitude of the gradient of the tensor ellipsoid constant over the surface?

The following is from Lagrangian Dynamics by D.A. Wells: It can be shown that the direction cosines $l,m,n$ of a line drawn normal to the surface $\phi\left[x,y,z\right]=C$ are proportional to $\...
0
votes
3answers
52 views

Why does the force of a torque applied on a cylinder of mass $m$ at an arbitrary point equal to $F=ma$ circumference?

For the question I attached I can't seem to understand one part of it and my friend and teacher can't seem to explain it too. I've included the solution with my understanding of what's happening. The ...
0
votes
1answer
29 views

Angular SHM and center of mass

This has been confusing me for a while. Consider a solid, homogeneous rod of mass $m$ and length $l$, hanging from a fixed pivot. Its center of mass is located at $\frac{1}{2} l$, and its moment of ...
-1
votes
1answer
88 views

Violation of energy conservation during collisions of a particle with different sections of a rod [closed]

Imagine a homogenous rod with total mass $M$ and length $l$ floating in free space without any force or constraint acting on it. Then, think about two possible scenarios. In the first, a particle with ...
5
votes
2answers
432 views

How to find the axis with minimum moment of inertia?

If a system of particles is given, in a 2D plane, with particles having masses $M_1$, $M_2$, $M_3, \ldots M_n$ and coordinates $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3), \ldots (x_n y_n)$, then how can one ...
0
votes
2answers
53 views

Moment of inertia rotational mechanics

Moment of inertia of cube about body diagnaol is $ma^2 /6$. Moment of inertia of cube about any axis passing through centre of mass is same only. Is this result correct? If yes how do we prove that $...
1
vote
1answer
40 views

In which scenarios is the derivative of mass moment of inertia ignored and taken into consideration for rigid bodies?

When taking the time derivative of Angular Momentum The first two terms represent the relative rate of change with respect to the coordinate system used. Most sources I have been reading state that ...
3
votes
3answers
66 views

Why do vehicles with a higher center of mass roll more easily considering that they have a higher moment of inertia?

It is a well known fact that cars with a higher center of mass roll over more easily, but why is this true considering that higher center of mass = higher moment of inertia? I understand that the ...
1
vote
1answer
46 views

What is the definition of the moment of inertia tensor?

I can find volume integrals for the moment of inertia in 2D and 3D, but is there a definition that works in an arbitrary number of (spatial!) dimensions?
1
vote
3answers
158 views

How is it possible to calculate the moment of inertia?

I would like to calculate the angular acceleration of an object on which a force $F$ is applied at point $P$. The scene is 2D, and the complex object consists of many axis-aligned rectangles. I ...
1
vote
1answer
41 views

Uniqueness of Mass Moment of Inertia tensor

I was curious to know if there can exist two different objects (shape and/or mass distribution) that can have the same inertia tensor.
-1
votes
3answers
94 views

Is Moment of Inertia, always, independent of angular velocity? [closed]

I once heard in a ted talk that the elementary particles like electron and proton can exist in two different positions at the same time. Now,I'm trying to understand a rotating rod from this ...
1
vote
2answers
212 views

Is it always true that a solid object(geometrical figure) has less moment of inertia than its corresponding hollow one? [duplicate]

what I mean is that,if you have two objects(one hollow and other solid): Lets say, a solid sphere and a hollow sphere and if you calculate moment of inertia of the two of them, you would find that ...
0
votes
0answers
61 views

What's the rotational inertia of a tetrahedron at the origin?

The Problem What is the inertia matrix, about the origin, for a tetrahedron $OABC$, where O is the origin, and A, B, and C are arbitrary points in 3D space, with a density of $1 kg/m^3$? What I ...
1
vote
0answers
100 views

How do I convert cardinal axis inertias to an arbitrary axis inertia?

I've tried to reduce this problem to the most basic form. I know the equation for a spring-mass system is generally: $$ F_{\mbox{applied}} = kx + m\ddot{x} \\ $$ but, in my case, I have a spring ...
4
votes
2answers
329 views

Moment of inertia: why $\mathrm dI=r^2\mathrm dm$ instead of $\mathrm dI=m\mathrm dr^2$?

When computing the moment of inertia, I observed that people usually use the following logic: $d I=r^2 dm,\ \therefore I=\int r^2 dm$ My question here is, why not use $dI=m ~d(r^2)$? I ...
4
votes
2answers
73 views

Would a force not cause acceleration $a=\frac{F}{m}$ if part of it is used to cause rotation?

Let's say we have a massless rod of length $2\,\mathrm{m}$ that has a $1\, \mathrm{kg}$ ball at one end and another $1\,\mathrm{kg}$ ball at the other end.$$ \begin{array}{c} {\displaystyle{~\large{{\...
-2
votes
1answer
112 views

Pendulum hanging from moving wagon [closed]

My Question is: What is the equation describing the angle of the pendulum (theta) depending on the time depending position of the wagon(x(t)). theta( t, x(t) ) = ? Note: Neglecting any sort of ...
2
votes
2answers
78 views

balancing a weight on a table without tipping over

I have a statics problem. Here is a model for a table: a circle of radius 1.5 ft a pole in the center a base in the shape of an X. I place a weight on the table on the edge. How much weight can ...
1
vote
1answer
373 views

Magnet can spin the fidget spinner, Why?

I have noticed that a small neodymium magnet can get my fidget spinner going at a relatively low velocity compared to what I can get from the force of my finger. I think I know why it is possible to ...
0
votes
1answer
93 views

How do you calculate the moment of inertia given the mass and final velocity of a hollow sphere?

The equation for the moment of inertia of a hollow sphere is I = 2/3mr^2. However, the radius is unknown and I am only given the mass and final velocity of a hollow sphere rolling down a ramp. How ...