# 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.

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### Is Energy conserved in a spinning top?

When we spin a top (give it kinetic energy $K_0$) and place it on a table, it starts precessing around the vertical axis. Is the total energy of the spinning and precessing top equal to the initial ...
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### Angular Velocity in the Plane of a Lamina

A rigid body (i.e., a 2-dimensional object) has principal moments of inertia about the centre of mass of $I_1 = (\mu^2 -1), I_2 = \mu^2 + 1, I_3 = 2\mu^2.$ I wish to show, using the Euler equations, ...
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### Weird rotational motion of a heavy thick disc

I and my friend noticed a strange behaviour of a rotating disc (or a cylinder) and we don't know how is that happening. This is the video. Actually what is happening in the video is that the disc ...
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### Why do we use $\Delta m$ in the derivation of angular momentum of a rigid body?

while I was watching a derivation of angular momentum of a rigid body on youtube, it came to my attention that the person who was doing the derivation, used $\Delta m$. my question is, why did he use ...
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### Addition of forces on a rigid body instead of a point

When two forces act on a point mass,we add the forces like we usually do and i have no problem understanding that. When the same forces are applied on a rigid body,how are we able to add them the same ...
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### In a rigid body rotating in 3D around the origin, is the norm of the linear velocity of each particle constant?

I was trying to prove that kinetic energy is constant in a rigid body undergoing some arbitrary rotation around the origin in a 3D space, and I ended up proving a stronger statement: that the norm of ...
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### Is a free rigid body in 3D space an integrable system? [duplicate]

I am trying to find three integrable systems with 6 degrees of freedom using the Liouville–Arnold theorem. That means that a set of integrals of motion that correspond to a conserved quantity for ...
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### Euler's equation of motion for rigid bodies rotating with one rotation axis not through the body's center of mass [closed]

this is my first question in this forum. Thanks for all the knowledge and support shared throughout the whole website! I have a body with rotations around 3 axes. I am looking for the external torques ...
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### How to transform Arbitrary Rotation Matrix $A$ to a coordinate system where the $z$ axis lies along the axis of rotation by Similarity Transformation?

In Chapter 4 of the book Classical Mechanics by Goldstein, it was written that "By means of some similarity transformation, it is always possible to transform the matrix A to a system of ...
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### Moment of Inertia of a screw rotating on a horizontal plane [closed]

Since a screw is kinematically equivalent to a cone, you can consider it like one, but I wanted to mathematically model the motion of a screw/cone as it is rotating on a plane. However, the moment of ...
205 views

### Kinetic energy in combined rotational and translational motion

If a body is free to move I have studied that any point can be assumed to be in translational motion with velocity of the centre of mass along with a pure rotational motion with $\omega$. For Kinetic ...
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### How does the parallel axis theorem explain the opening of a door?

As I get closer and closer to the hinges of a door, it becomes harder and harder to open. However, the distance to the hinges is getting smaller and smaller, where the rotation is occurring. All the ...
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### What illustrative example of the central axis theorm exists? This is not the parallel axis theorem

This is from Ira Freeman's translation of Georg Joos's Theoretical Physics. I've taken a few liberties with the notation. It may be shown also that there is always an axis such that if any point ...
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### Why would a hollow cylinder lose a race with a solid one?

Apart from the physics stuff which clearly shows why the hollow cylinder will lose: $T = RF = Iα = I* a/R$, since both F and a are missing we use the second equation F = ma: Here are the forces ...
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### If torque is not observer dependent for bodies in translational equilibrium then why doesn't the angular acceleration change?

I know that if a body is translational equilibrium then torque about any point is zero and have also understood it's proof. My teacher had told me that angular acceleration about any point will be ...
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### Work of the contact action of a force on a wheel

I have a question regarding wheels. Suppose I have a skateboard with perfect bearings, and I live in a world without air. At $t=0$, it is on the ground and I give it some initial speed, $\vec{v}_0$. ...
63 views

### Rolling motion in space [closed]

Is rolling motion possible in space? If so, Let's imagine that two cylinders of different masses and inertias were rolled over an incline in space is it the case that the one with lower inertia will ...
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### Center of rotation of a rolling screw

So I was just researching into the motion of a screw as you try to roll it on a surface and I observed that on applying a force/pushing it, the screw moves in a circle like a cone would if you were to ...
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### Doubt regarding cancellation of internal torque for a rigid body (Kleppner and Kolenkov) [duplicate]

In chapter "Dynamics of fixed axis rotation", the book says newton's laws are not enough to show that the internal torques of a rigid body cancel out. But section 1.2 in Goldstein says that ...
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### What does it mean to take a mass moment of inertia about a single point?

This website here: https://www.chegg.com/learn/calculus/calculus/moment-of-inertia-about-the-origin Shows the following: How is it possible to define a mass moment of inertia about the origin which ...
188 views

### Ball rolling in a cylindrical trough

I am trying to understand an interesting effect I observed while playing with my kids' toys (video). The energy in this system seems to slosh back and forth between the trough and the ball, with the ...
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### Derivation of the Lagrange equations of motion from d'Alembert's Principle specifically for rigid bodies

All of the proofs of the Lagrange equations of motion from d'Alembert's Principle I've seen so far deal exclusively with the force-inertial force balance for particles ($F-ma=0$). Despite this, the ...
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### How to prove law of mass conservation? [closed]

In our mechanics class, we began to discuss rigid movement. Let me begin with our definitions. Definition 1: A map $f: D \subset \mathbb{E}^3 \to \mathbb{E}^3$ is rigid, if it preserves distance ...
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### Estimating angular velocity of rigid body via position

Suppose you have current state of a rigid body is $S_t = [\theta_t, \phi_t, \psi_t]$ and your past state is $S_{t-1} = [\theta_{t-1}, \phi_{t-1}, \psi_{t-1}]$ How would you estimate angular velocity ...
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### Why don't Euler's formulas for torque apply to this problem?

In my mechanics class we were assigned problem 9.44 from "Introduction to Classical Mechanics" by David Morin as homework. The problem and figure are below: Two wheels of mass $m$ and ...
32 views

### Can the angular velocity of a prolate spheroid change over time in the absence of external forces?

Given a prolate spheroid (ie a Rugby Ball/American Football), with an initial angular velocity about an axis that coincides with one of the shape's primary axes, it seems obvious that in the absence ...
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### Rigid body motion in Arnold's book

During the study of the motion of a rigid body, in Arnold's book, two coordinates systems are introduced: one is fixed $k=\{O',\hat e_1',\hat e_2',\hat e_3'\}$ and one is inside the rigid body \$K=\{O,\...
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### What would it feel as a human being to experience the Dzhanibekov Flip?

The Tennis Racket theorem describes the following effect: rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate ...
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