# 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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### Why isn't the moment of inertia of a cylindrical tube the difference of those of two cylinders?

The moment of inertia of a solid cylinder is $\frac{1}{2}mr^2$, and the moment of inertia of a composite object is the sum of the moments of inertia of the objects it consists of minus the moment of ...
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Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in ...
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### Why does a free body rotate about centre of mass when torque is applied? [duplicate]

Suppose a body is kept in space and is not fixed about any point (i.e, not hinged). If an external force is applied, the body rotates about the centre of mass. I saw one answer pointing out that ...
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### Do magnetic fields cause rotational inertia proportional to their magnetic moment?

If I have a stick that has a spinning disc on the end of it, and I try to rotate the stick, I will feel more inertia the faster the disc is spinning because I have to transform its rotational energy ...
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### Very Basic Question: Calculation of Moment of Inertia Tensor

I am studying from the book Classical Dynamics: A Contemporary Approach by Jose & Saletan, and at page 496, they work through an example about the moment of inertia tensor of a uniform cube (sorry ...
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### Principal Axis and Conservation of Angular Momentum

In the video, the rotation of the wooden block around the principal axis with intermediate moment of inertia is an unstable rotation, where the axis of rotation and therefore the angular velocity ...
1 vote
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### Why does MOI of rectangle depend on length of diagonal of the rectangle? [closed]

If we have a rectangle of length $a$ and width $b$ my physics textbook showed that the MOI about the axis of rotation in the picture is given by \begin{align}\label{MOI rectangle} \dfrac{1}{12}M(a^2+...
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### Why does the centrifugal force act normal to the surface?

This questions comes from understanding the Tennis Raquet's Theorem, also known as Dzhanibekov's effect in this video: Veritasium's video On the second 8:36, we can see that when they try to add some ...
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### Inertia tensor for spinning top

I was trying to find the equations of motion of a symmetric, solid and fixed spinning top employing Euler's angles and lagrangian mechanics. As for Euler angles I used the following convention (the ...
1 vote
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### Question about product of inertia of rolling disk [closed]

If a uniformly distributed mass, as a perfectly symmetric circular disk, performs a rolling motion or trans-rotational motion on a stationary plane, with $\alpha$ angular acceleration about it's ...
1 vote
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I am brand new here. I am a furniture maker and designing an Oval Pedestal Table for a client. I presented a design that I felt comfortable with, however my client has asked that I shrink the ...
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### What is the total kinetic energy of a pendulum?

I have a sphere of a mass $m$ and radius $r$, attached to a massless string with a length $l$. The pendulum moves with an angular velocity $\omega$. I know that axes of rotation can be relative. If I ...
1 vote
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### Calculating moment of inertia for a hollow cylindrical shell of varying amounts of water within it for an experiment about rotational motion [closed]

I am doing an experiment with the overall research question of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane I was ...
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### Why distance in Moment of Inertia definition arises squared? [duplicate]

The moment of inertia is defined as: $$I=\int_{}^{}r^{2}dm=\int_{}^{}r^{2}\rho dV$$ While it is obvious from the experience that the father away the mass from the axis of rotation the more it adds to ...
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### Energetics of a Discus Throw

When a discus thrower releases the discus, the discus will have a certain forward speed that will be the same as the thrower's rotational speed multiplied by the distance between the thrower's center ...
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### Inertias of the drivetrain components of a 4x4 vehicle or any geared system for that matter

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 =...
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### Deduction of mass moments up to the fourth order

Could anyone show me the details on the deduction of a discrete object's zeroth, first, second, third and fourth mass moment? For example, for the hydrogen fluoride with symmetry $C_{\infty V}$? I ...
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### Query regarding parallel axis theorem

Suppose there are two points at (4,0) and (-4,0) each of mass 1 kg and the origin is (0,0). The rotational inertia of the combined system is 32kg.m^2. But if we shift the axis of rotation to left by 2 ...
1 vote