# Tagged Questions

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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### How does this dumbbell rotate?

I am reading the book Spacecraft Attitude Determination and Control by J.R. Wertz, and on page 488 it says: My question is: how does the axis of rotation, $\hat{\omega}$, rotate? How does ...
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### Principal moment of inertia for a rotating body

My major is not in physics. I am reading the following paper: (my problem is simple and not related with any optimization) http://arxiv.org/abs/1410.2841 (p.5~p.6) Suppose The ...
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### Simple Disk rolling with slipping on a horizontal plane

This is the first time I've encountered this scenario. I want to understand how to handle it. Since the disk is slipping, what would be the work done by the frictional force? What is the ...
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### Work done by internal forces of a rigid body

I am reading Goldstein's Classical Mechanics book, and I came across that: In a rigid body the internal forces do no work Is this statement based on the assumption that the internal forces are ...
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### Stuck with 2D kinetics problem [on hold]

I've been trying to solve this exercise for the last four hours and I'm totally stuck. The problems goes like this: Given the mechanism in the image, located in the vertical plane, the OB cord ...
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### Kinematics of Rigid Body [on hold]

I'm working out in this problem since last week but I'm not able to identify how to calculate the total angular momentum. Can anyone help me? A uniform disk of mass $m$ and radius $r$, mounted on a ...
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### Rolling Coin (Old Physics Quals Exam) derivation help [duplicate]

I am trying to understand the derivation for the angular velocity of a rolling coin in the problem given on this website: http://functionspace.com/question/27/answer/121 How does one find angular ...
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### Is it possible to throw a stick without giving it a rotational motion?

When walking with our dog I always throw wooden sticks for her. Then one time I wondered if I could throw the stick (normaly, so not like a spear) without imparting on it a rotational motion around ...
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### What is intertia tensor for tapered cylinder (solid and with separate inside and outside radii)?

I need the inertia tensor for tapered cylinders, both solid and hollow, and if possible with independent inner and outer radii on the $x$ and $y$ axes (so the cross-sections of the cylinders can be an ...
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### Verifying directions of forces during pure rolling?

Let us take a cylinder on a rough horizontal surface. The cylinder undergoes pure rolling A vertical downward force acts on the cylinder to produce a clockwise rotation. The point at which it acts ...
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### Rigid body problem in 2d

I have some questions about this exercise: In an horizontal plane, a $OA$ bar with mass $m$ and length $a$ moves, with another bar $AB$ (same mass, double length) attached in the point A. In the ...
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### Why falling camera/objects rotate and then stabilize?

I was going to ask something very similar to this question (which hasn't been answered). Basically a camera fell from an airplane and it began to rotate (maybe because initially it was put in rotation ...
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### How do I treat the Lagrangian in the case of a rigid body?

Here's Exercise 1.11 from Goldstein's Classical Mechanics 3rd edition (the first one after having derived the Lagrangian basically): Exercise 1.11: Consider a uniform thin disk that rolls without ...
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### Two Rolling logs

Suppose we have two logs rolling down a hill, one of gold and the other of wood; the acceleration for both will be equal, something which is unclear to me; I get that this may be due to their form, ...
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### Rotation of a rod due to a normal force

Suppose there's a rod suspended in space free from the effect of any force. Let a force F act at a distance x from one end. How can i prove that rotation will take place about an axis passing through ...
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### Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm $OA$. ...
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### Which is the axis of rotation?

This should be simple, but it keeps bothering me. If a rigid body has no fixed axis, and a torque (defined relative to a point $A$) is applied, it will rotate around $A$. But often I can also ...
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### Rotational work and forces such as static friction or ropes tension

I'm confused about the rotational work, defined as $W=\int_{\theta_1}^{\theta_2} \tau_z d \theta$ Where $\tau_z$ is the component of the torque parallel to the axis of rotation $z$. Consider a ...
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### instantaneous velocity center

The instant center of rotation, also called the instantaneous velocity center is the point fixed to a body undergoing planar movement that has zero velocity at a particular instant of time. For ...
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### Is there a form of rigid body dynamics that uses unit quaternions instead of Euler angles?

I’d like to know specifically about an elegant way of deriving a second derivative of an orientation quaternion from a torque and a moment of inertia matrix, if one is available. The straight forward,...
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### Why does a rigid body rotate and not simply translate when pushed with an instantaneous force?

Let's say we have a metal rod of consistent density sitting flat on a frictionless surface. I intuitively understand that if I push one of its ends away from me, (at a right angle to the length of the ...
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### What's behind the moment of inertia and other “body-global” properties of bodies?

I'm an electrical engineer currently doing some (computational) mechanics stuff. In introductory literature about mechanics, you can read plenty about the moment of inertia and how you use it in ...
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### Conceptual understanding behind moments of force for a rigid body cylinder

I have a question behind the conceptual understanding of the following equation: $$\frac{\text{d}}{\text{d}t}\mathbf{L}_G = \sum_i \ \mathbf{r}_i\times \mathbf{f}_i$$ where $\mathbf{L}_G$ is the total ...
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### Differential equation of motion of combined rigid body

I am reading the following paper: http://tinyurl.com/jv2pu2m I have a question about (1) and (2): To (1), I think the following link provides good explanation. Equation of Motion for Rigid ...
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### degree of freedom of a rigid body 5 or 6?

I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only ...
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### Finding the Mass of a Precessing Top

Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular ...
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### Area moment motivation

I have some intuition about the (second) moment of inertia, and there is some motivation to define this concept if we think about the $KE$ of a rotating body or the torque $\tau$ applied, for example, ...
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### Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
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### Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ...
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### rigid body dynamics - equations of motion if CM coordinate system not coincident nor aligned with body axes

My goal is to find inertial expressions for velocity and displacement components for a satellite subjected to an external torque (from a thruster aligned to the body system). I've reviewed some texts ...
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### Velocity of the points of a rigid body

The most general motion of a rigid body is a roto-traslation. Firstly is it correct that any point (let's call it $O$) of the rigid body can be seen as the point through which passes a istantaneous ...
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### Spinning top fixed point

I have seen many explanations about the movement of a spinning top. The explanations were in a varied level, from basic newtonian mechanics to Lagrangian formalism. But I do not understand why some ...
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### Where is the mistake in the following rationament [duplicate]

Well... kind of hard to translate in English so bare with me :). Let's consider a wheel that spins in the void. Each point of the wheel has the speed $v = ω r$. That means that for any $ω$, there is ...
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### How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
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### Finding $\theta$ at any point in time [duplicate]

I am looking to simulate the movement of a steel beam which has a constant mass $m$, and that has a pivot $O$ at one end that is moving with a constant horizontal velocity with magnitude $v$. ...