# Questions tagged [moment-of-inertia]

The moment of inertia, or rotational inertia, determines the torque needed for a desired angular acceleration about a rotational axis. Like inertial mass is the resistance to being linearly accelerated, the moment of inertial is the resistance to being rotationally accelerated.

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### How does attaching a point mass to the CM of an object affect its moment of inertia about the CM?

How does attaching a point mass to the CM of an object affect its moment of inertia about the CM? Intuitively, it seems to me that this would not affect the mass distribution about the center of mass, ...
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### Why can't we use integral of $x$, $y$ and $z$ in calculating moment of inertia

I've got no problems with calculating the moment of inertia/tensor of inertia of a cube using an integral over the lamina of a cube. However, I must be missing something obvious or making some sort of ...
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### Are there physics theorems that can prove maths theorems? Eg Pythagoras' Theorem

There's this recent post on maths overflow Which theorems have Pythagoras' Theorem as a special case? that has an answer by dxiv that appears to use a physics theorem to a prove a maths theorem, ...
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### How do the inertia tensor varies when a rigid body rotates in space?

The inertia tensor is clearly constant the in a frame moving with the rigid body. But what is the simplest way to see why its columns can be considered rotating vectors in space with the angular ...
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### Moment of Inertia of a solid hemisphere. What am I doing wrong? [closed]

I want to calculate the MOI of a uniform solid hemisphere about Axis passing through its centre of mass (COM) and perpendicular to the circular base. Axis coinciding with any diameter at the ...
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### Question on the proof of Moment of Inertia for a solid sphere

I was trying to prove myself the moment of inertia of a solid sphere. Here's it, Let us consider a sphere in $3$-dimensions with radius $R$ and mass $M$. Moment of inertia is the product of mass with ...
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### Inertia tensor for rotors

For vectors we can use Inertia tensor. But if I want to use bivectors (Rotors), what should I use for the inertia tensor? I want to make a 2d game and progressively to 4d.
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### Inequivalence of 2nd Moment of Mass and Moment of Inertia

My question is concerned with the difference between two ways of defining the moment of inertia, and how to interpret the difference. Let me begin by saying I understand moments of inertia are ...
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### Moment of inertia when velocity is zero

The most basic form of the moment of inertia comes from fix axis rotation, that is $$L=\int rv\, dm=\int(r\omega)(r\,dm)=\omega \int r^2\, dm\tag{1}$$ Here $r$ is the perpendicular distance from the ...
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### Doubt on the application of conservation of angular momentum

The following is the picture from the you tube channel physics desmos. In this the man is demonstrating the conservation of angular momentum. Now the explanation of it is also given in my book as ...
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### What's exactly is moment of inertia?

I know that angular momentum can be expressed in terms of moment of inertia tensor as follows, $$\vec{L}= I_{\text{tensor}}\vec{w}$$ Where $I_{\text{tensor}}$ is tensor for moment of inertia. It can ...
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### Does the angular velocity of a rotating rod change when its axis of rotation changes?

If a rigid rod of length $l$ rotates on one end around the origin with an angular velocity of $\omega$ and suddenly the end fixed to the origin is released allowing the rod to move freely without any ...
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### Will an object undergoing translation move faster than if it underwent both translation and rotation?

So I'm revisiting my physics, as I'm looking to solidify my foundations. I was going over the chapters concerning rotation of rigid bodies and I just thought of this problem: If an impulse is applied ...
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### Moment of Inertia of solid cylinder about the exist through it centre and perpendicular to its axis of cylindrical symmetry

I have seen the derivation of it first we find the moment of inertia of the disc about its diameter: I =(MR²/4l)dx and then we apply the parallel axis theorem <...
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### Can anyone guide me on torque equation to rotate a part?

hope you all are doing good. I am a bit confused on which equation to use to calculate the torque required to rotate a part. I want to use a hydraulic motor at the 6th axis (end of robot arm) of ...
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### Why is mass changed for moment of inertia in the formula for rotational kinetic energy?

The linear kinetic energy is $$\frac{1}{2} \cdot m \cdot v^2$$ and the rotational kinetic energy is $$\frac{1}{2} \cdot I \cdot \omega^2$$ Why is mass changed for moment of inertia in the equation for ...
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### Moment of Inertia of Triangular loop made of rods only about an axis passing through one of the vertex and in the plane of loop parallel to the base

This question is from electrodynamics although I am stuck in the mechanics part here. $AB$,$BC$,$CA$ are wires/rods, we needed to calculate Moment of Inertia(MOI) about an axis $xx'$ parallel to BC ...
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### Regarding simple pendulum

When I was going through the wikipedia article I have read clock pendulums are usually made of a weight or bob attached to the bottom end of a rod, with the top attached to a pivot so it can swing. ...
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### Moment of Inertia of a Rectangular Parallelepiped

Moment of inertia calculated about an edge for a rectangular parallelepiped is given by $$I = (m/3) (a^2 + b^2),$$ my question is: when m(a^2+b^2) is added to I, the new value obtained is Moment of ...
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### Question regarding $ΣM= Iα$ and an example problem given by my professor

In this example problem, an applied moment and two hanging masses of different values and in different positions caused a double pulley to rotate and angularly accelerate. As you can see, on the ...
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### Why do objects with lower rotational inertia have more translational kinetic energy?

In my physics class, we have seen experimentally that objects with lower $I$ values (like spheres) will reach the bottom of a ramp sooner and with a higher final velocity than objects with higher $I$ ...
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### Can passing an alternate current through an inductor be compared with speeding up and then slowing down a very massive object?

Can passing an alternate current through an inductor be compared with speeding up and then slowing down a very massive object? So, for example, when a capacitor discharges through an inductor the ...
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### Moments of inertia

I know the concept of moment of inertia from $L=I \omega$, $\tau =I \alpha$, $I=mr^2$, and so on. I also know the that, in general, $I=\int r^2dm$ I would like to know how we derived the moments of ...
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### Does moment of inertia tensor keeps changing if object is rotating about multiple axes?

Consider a plane circular disc kept in X-Y plane with Z axis passing through its centre. It is rotated about all threes axes with some angular velocities. In such a case, to find the inertia tensor, ...
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