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 ...
2
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1answer
25 views

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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1answer
40 views

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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2answers
47 views

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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0answers
24 views

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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0answers
36 views

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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0answers
32 views

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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1answer
75 views

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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1answer
138 views

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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2answers
49 views

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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1answer
427 views

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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2answers
245 views

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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1answer
393 views

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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3answers
55 views

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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1answer
35 views

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 ...
2
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5answers
388 views

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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3answers
3k views

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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2answers
89 views

Horizontal rolling without slipping

I'm trying to find the friction coefficient that makes the body roll without slipping but I just can't reach a value. The force is applied on a small central disk of radius $r=0,03\, m$ and mass $m=0,...
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1answer
68 views

Tangential Velocity of a Rotating Rod

I have the following question which has given rise to a doubt. One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no resistance. ...
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1answer
20 views

Frictional torque=? [closed]

A uniform, hollow, cylindrical spool has inside radius $R/2$, outside radius $ R$, and mass $M $ (see figure below). It is mounted so that it rotates on a mass less horizontal axle. A mass m is ...
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1answer
41 views

How to find the axis of rotation or location given the angular velocity?

Say I have the angular velocity vector of a body as a function of time. How can I determine the axis of rotation/location of the body? we have the equation: $\frac{d\vec{r}}{dt}=\vec{\omega}(t)\...
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2answers
93 views

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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1answer
37 views

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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0answers
31 views

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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7answers
183 views

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 ...
2
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2answers
46 views

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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2answers
37 views

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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1answer
54 views

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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2answers
4k views

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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1answer
34 views

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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2answers
130 views

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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1answer
44 views

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 ...
2
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0answers
133 views

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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0answers
22 views

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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2answers
31 views

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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1answer
44 views

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 ...
1
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1answer
76 views

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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2answers
487 views

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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0answers
54 views

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 $v$. ...
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1answer
843 views

Defy gravity torques with gyroscopes?

Context On the following drawing, a platform is hung from the ceiling not exactly from its centre of gravity. Because of this it can't sustain an arbitrary orientation for long; I want to increase ...
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0answers
75 views

Euler's equations (rotating frames)

I'm trying to understand the Euler's equations and I'm having problems with rotating frames and on which specific frame is each quantity measured. On the equation $$ \left(\frac{dL}{dt}\right)_{...
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5answers
118 views

Rolling without slipping taking the contact point as pivot

I'm confused about this "rolling without slipping" kind of situation. Or better in this case the object is rolling and slipping, just use the label "rolling without slipping" to identify the kind of ...
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3answers
82 views

Rotation of rigid body with two different angular velocities

Consider a cylinder that rotates about a vertical fixed axis with angular velocity $\vec{\Omega}$ while rotating about a vertical axis passing through its center of mass with angular velocity $\vec{\...
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1answer
39 views

Principal axis of inertia parallel to the ones passing through the center of mass

Consider a rigid body and the (at least) three axes of inertia passing through its center of mass. Will any other axis not passing through the center of mass but parallel to one of the principal axes ...
2
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1answer
57 views

Parallel axis theorem and Koenig theorem for angular momentum

Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics? The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$ Koenig theorem ...
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2answers
115 views

Forces that exert torque on a rigid body in rotation when angular momentum is not parallel to angular velocity

I'm confused about the rotation of a rigid body, when the angular momentum $\vec{L}$ is not parallel to the angular velocity $\vec{\omega}$. Consider a barbell with two equal masses that rotates ...
0
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1answer
27 views

Derivative of angular momentum of rigid body

I found this equation that describes the change in angular momentum $\vec{L}$ of a rigid body rotating about a fixed point $O$. $I_o$ is the moment of inertia of the body with respect to the axis of ...
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1answer
20 views

Angular velocity and velocity of CM indipendence in rigid body motion

In the most general case, in rigid body motion the linear velocity of the center of mass $v_{cm}$ and the angular velocity of the rigid body $\Omega$ are not related with each other. Which condition ...
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3answers
90 views

Rolling without slipping in absence of friction force

I'm confused about a rolling without slipping situation. Suppose to have a disk of radius $R$ on a floor, and exert a horizontal force at a certain distance $r$ from the center of mass. I would like ...
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1answer
22 views

Calculation of support reaction in rigid body rotation and collisions

I can't understand the logic behind the calculation of torques exerted by supports in rigid body motion, especially rotation. The equation of angular momentum is $$\vec{\tau}=\frac{d\vec{L}}{dt}\tag{...