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.

0
votes
0answers
36 views

I am confused about moment of inertia

Question There is a homogeneous and nonelastic (solid) rod on the frictionless line with mass M, length L and velocity V. Then line becomes a circle with radius L and our rod starts turning around it. ...
0
votes
0answers
33 views

Moment of intertia of a trinagle pendulum [on hold]

Find the moment of inertia of 3 rods with mass m and length L connected to form a triangle. The axis of rotation is that of a pendulum. The moment of inertia of a single rod with the axis through its ...
0
votes
1answer
21 views

Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
0
votes
1answer
35 views

Kinetic energy of a yoyo

Consider the yoyo above: The yoyo is constructed from two heavy disks of radius R connected by a light axle of radius r , as shown in the figure below. The total mass of the yoyo is M and its moment ...
1
vote
1answer
40 views

Angular momentum w/ changing moment of inertia

A man of mass m1 is standing on a disk with radius R and mass M at a distance r The man starts walking around the disk with constant angular speed w1 and as a result the disk begins to rotate in the ...
1
vote
1answer
33 views

Does the moment of inertia scale quintically for similar solids?

In this list https://en.wikipedia.org/wiki/List_of_moments_of_inertia there appears to be the pattern that the moment of inertia of a similar solid scales quintically. For example, given a sphere of ...
1
vote
2answers
123 views

An illogical argument in Goldstein while deriving the Euler's equation(s)

In the book of Goldstein, at page 200, the author argues while deriving the Euler's equation(s) that $$\left.\frac{d\vec L }{dt }\right|_s = \vec \tau,$$ where subscript $s$ denotes the space frame. ...
0
votes
1answer
43 views

Moment of Inertia of a semi ellipsoid?

I understand that mass is simply found by taking the integral of $\rho$ and differential volume. I just do not understand how you can take the del of $I_x$ and where that equation $y^2\text{d}m/2$ ...
-1
votes
1answer
31 views

Homework problem on pulling a rotating cylinder wrapped with massless rope [closed]

I am trying to solve the following homework problem on mechanics. The solution I attempted is as follows. Equations of motion for cylinder: $F=ma $ $\rightarrow$ $100N=20kg \times a$ $\...
0
votes
1answer
42 views

Angular Momentum vs Kinetic Energy [closed]

Suppose we have a spinning top, with angular velocity $\omega$, its speed is null and there is no force applied to it. Let $J$ be its moment of inertia. We can say $E_k = \frac{1}{2}J\omega^2$ and $L ...
-1
votes
1answer
62 views

How did moment of inertia affect the length of the day? Please try to explain briefly [closed]

How did moment of inertia affect the length of the day? Please try to explain briefly.
0
votes
1answer
18 views

Gravitational Potential Energy between points on a disk

So if I wanted to calculate the potential energy between two points on a disk, would I just use the formula for Gravitational Potential energy? if so, what would be the mass? Would I use some form of ...
1
vote
1answer
46 views

inertia tensor of rigid body in generalized coordinate frame?

Assuming we know the inertial tensor of a homogeneous rigid body about a coodinate frame at its COM and aligned to it principal axes, how do we find the inertial tensor for the body in some other ...
0
votes
2answers
58 views

Center of mass and moments [closed]

I got part $(i)$, but got stuck on part $(ii)$. For part two, I know that I have to take the moments about the center of the base of the cylinder (let's call that $\text{O}$) I know that the center ...
0
votes
3answers
70 views

Moment of Inertia Race [closed]

Wikipedia shows an example of how to the moment of inertia determines how fast a rotating object rolls down an incline plane. the race Includes: spherical shell, solid sphere, cylindrical ring. solid ...
0
votes
3answers
36 views

What happens to moment of inertia if a body is divided into 2 congruent part?

If a circular disk is cut in half, and a square plate is divided into 2 identical right angled triangle, when the axis of rotation is not changed i.e if the square plate was rotating about an axis ...
-2
votes
1answer
31 views

Will moment of Inertia vary with size? [closed]

I have a very basic question. What will happen to the moment of inertia if the object is uniformly shrunk? For example assume a rectangular beam and shrink all the dimensions uniformly. Will the ...
0
votes
0answers
36 views

Transform an Inertia Tensor

I am trying to provide colleagues with a spreadsheet method of transforming the inertia properties of a complex shaped body to a different coordinate system, involving only rotation. I've read that ...
0
votes
0answers
29 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
50 views

Moment of inertia and torque [closed]

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 ...
1
vote
1answer
37 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
87 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
157 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
38 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
171 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
43 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
91 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
66 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
61 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
70 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
152 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
89 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
110 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
28 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
21 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
77 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
65 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
69 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
343 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
180 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 $z$-...
-1
votes
1answer
60 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
61 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
31 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
640 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 ...