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Questions tagged [rigid-body-dynamics]

The study of the movements of a collection of connected bodies subject to external forces in the absence of deformation. This tag should be used for questions on the analysis of 2D/3D dynamics of rigid bodies, do NOT use this tag because your question contains a rigid structure.

Rigid-body dynamics is the study of the movements of a collection of connected bodies subject to external forces in the absence of deformation. The assumption of a rigid body (no deformation) allows the dynamics to be described by translations and rotations, with the Euler angles often playing an important role in the analysis.

Typically, questions about rigid-body dynamics involve either a single solid object rotating about an arbitrary axis or a set of solid objects moving due to an external force.

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What do people actually mean by "rolling without slipping"?

I have never understood what's the meaning of the sentence "rolling without slipping". Let me explain. I'll give an example. Yesterday my mechanics professor introduced some concepts of rotational dynamics. When he came to talk about spinning wheels…
pppqqq
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Why does this object periodically turn itself?

See below gif image taken from here. Or see this Youtube video about 30 sec in. Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? Is there a simple equation that models this…
pacó
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Why don't helicopters use reaction wheels to counter the main rotor?

As the main title says. I'm finding myself wondering about helicopters. The tail rotor is a vulnerable and key piece of equipment, especially on military helicopters. I know some helicopters instead use two main rotors (for example the KA-50). Why…
Scuba Steve
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Stability of rotation of a rectangular prism

I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions seem more stable than others. The 3 axes which…
Kyle Oman
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Is it correct to say that it is theoretically impossible for perfect rigid bodies to exist?

If perfect rigid bodies were to exist, then consider a scenario in which two rigid bodies of equal masses moving with velocities of equal magnitude but opposite in direction colliding against one another. During the collision, the velocities of both…
Mathew_
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How can the contact point of a body rolling without slipping have zero velocity?

They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion?
Ashu Aman
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Why certain rotations are unstable? (Euler Equations)

We have the Euler equations for a rotating body as follows $$I_1\dot\omega_1+\omega_2\omega_3(I_3-I_2)=0\\ I_2\dot\omega_2+\omega_1\omega_3(I_1-I_3)=0\\ I_3\dot\omega_3+\omega_2\omega_1(I_2-I_1)=0$$ Where $I_i$ are the moments of inertia about the…
John Doe
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How to combine these equations of constraint?

I want to model a nonholonomic system of an arbitrary rotating disk in 3D, which rolls without slipping, and doesn't have to stay vertical. (think spinning a penny on the table) I want to use the method I just learned of Lagrange multipliers with…
user12029
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Why does a Yo-Yo sleep, and then awaken?

What are the mathematics / mechanics principles behind a sleeping Yo-Yo, and in particular, what changes with a wrist-snap flick that causes it to "awaken" and return to your hand?                         (Image from…
Joseph O'Rourke
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Does rigid body rotation contradict Newton's first law?

Per Newton’s law, an object will move along a straight line with a constant speed if no force is acting upon it. No portion of a rotating ball is moving in a straight line (except those on the axis which are static). How is it possible then that the…
aaa acb
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What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?

Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis which is perpendicular to the force and…
Alraxite
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Is there a quantum analogue of the "Tennis Racket" theorem?

A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is unstable. This is known as the "tennis racket"…
KF Gauss
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How can friction do no work in case of pure rolling?

I have read various answers, on PSE and elsewhere, and most of them explain that the point of contact of the rolling object undergoes no instantaneous displacement in the direction of friction, I agree, but then there is a feeling that the friction…
Aditya Prakash
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Will a pure rolling cylinder stop on a rough surface?

Will a disc or cylinder (rigid body) executing pure rolling on a rough surface stop, neglecting air drag and other heat losses and rolling friction but not static and kinetic friction? If yes, due to which friction it will stop, static or kinetic…
DarkSideofPhy
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Is there a rigorous equivalence between the ball-on-hemisphere and falling rod problems?

These are two well-known problems in classical mechanics that yield the same critical result: Problem 1: Ball on a Hemisphere A small ball of mass $m$ is placed at the top of a smooth (frictionless) hemisphere of radius $R$. An infinitesimal push…
Ruchin Himasha
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