Questions tagged [moment-of-inertia]

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Moment of inertia “about ? axis”

I'm just trying to calculate how fast a 2D polygon should spin given x amount of energy. To do this, I figured I'd split my shape up into triangles, calculate the MoI for each around the polygons ...
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How to calculate torque required move this cart? (Description) [on hold]

Weight of cart is 2kg It has two wheels on back, each if 6cm It's front half is in contact with surface and has kinetic friction coefficient = 0.75 The cart has to move at constant velocity 1m/s ...
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How to find moment of inertia about centriodal axis in easiest way?

Actual question is Find the moment of Inertia of the cross-sectional area of an I section about its centroidal axis: My solution: Here $A_{1}, A_{2}$ and $A_{3}$ are the areas: Centriod at X axis;...
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What is the significance of having two formulas for area moment of inertia?

What is the significance of calculating area moment of inertia twice? I mean calculating area moment of inertia w.r.t axis and calculating same area moment of inertia w.r.t centroidal axis? Why not ...
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How can a flywheel make engine run smoothly?

In the video Moment of Inertia Demo, a man states that moment of inertia will be higher if the masses are away from the axis of rotation. The engine take more power to spin the flywheel, because of ...
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Moment of Inertia for Arbitrary Shape

Consider any arbitrary shape with arbitrary rotation axes, global and or local to the shape that are able to describe any orientation of the shape. The shape is also defined with an arbitrary density ...
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Increasing Mass VS Increasing Force when pushing a Box [closed]

If we assume g=10m/s^2 & negligible friction The force needed to accelerate that box by 5m/s^2 would be 500N. This is a very basic one. The confusion came when an force of 250N (the force a 25kg ...
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Calculating the moment of inertia of a uniform sphere [closed]

Currently trying to calculate the moment of inertia of a uniform sphere, radius R, I know the answer is $\frac{2}{5}MR^2$ but I keep getting $\frac{1}{5}MR^2$ Setup: Assume mass per unit volume $\...
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Euler-Lagrange Equation and moment of inertia

I'm self studying and having trouble with the following question: "Consider a solid of revolution of a given height. Determine the shape of the solid if it has the minimum moment of inertia about its ...
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1answer
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Parallel axis theorem of stick-ball configuration

I have a system with a rod of mass m and length 2a. Let the origin be in the middle of the rod at x = 0. (Therefore, each end is a distance a away.) A ball of mass m is attached to the far right end. ...
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What actually is the vector of angular momentum?

If an object spins around a central point, it gets angular momentum which is a vector with an orientation dependent on whether its clockwise rotation or anticlockwise, i get that. But what the vector ...
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1answer
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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 ...
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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 ...
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1answer
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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 ...
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1answer
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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 ...
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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. ...
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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 $y^2\text{d}m/2$ ...
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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 $ $\rightarrow$ $100N=20kg \times a$ $\...
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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 ...
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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.
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1answer
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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 ...
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1answer
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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 ...
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2answers
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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 ...
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3answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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1answer
146 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 ...
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2answers
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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?
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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?
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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 ...
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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 ...
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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 ...
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1answer
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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. ...
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3answers
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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}{...
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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 $$I_{cm}=\frac{M{L^2}}{12}$$ ...
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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 ...
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1answer
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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 ...
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1answer
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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,...
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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\...
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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 ...
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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 ...
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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 ...
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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 ?
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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 ...
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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 ...