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.

learn more… | top users | synonyms

1
vote
2answers
85 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,...
1
vote
1answer
16 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 ...
0
votes
2answers
38 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 ...
0
votes
1answer
37 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)\...
2
votes
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,...
4
votes
7answers
170 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 ...
0
votes
2answers
36 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 ...
2
votes
2answers
45 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 ...
3
votes
1answer
50 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 ...
0
votes
1answer
34 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 ...
1
vote
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 ...
0
votes
0answers
21 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 ...
1
vote
1answer
39 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
vote
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 ...
0
votes
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 $v$. ...
0
votes
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)_{...
1
vote
5answers
108 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 ...
0
votes
3answers
65 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{\...
0
votes
1answer
32 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 ...
1
vote
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 ...
2
votes
1answer
54 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 ...
0
votes
1answer
26 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 ...
0
votes
1answer
21 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{...
1
vote
3answers
84 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 ...
0
votes
1answer
20 views

Ring Ascending a Step

Consider a thin circular ring of mass $m$, radius $r$ rolling without slipping with velocity $v$ towards a step of height $h$ $(<r)$. Assume no rebound and no slipping at the time of contact. What ...
1
vote
1answer
45 views

Why is the center of mass frame always used in rigid body dynamics?

In most of the cases the center of mass is chosen for rigid body motion description, but this is not an obliged choice, since the motion of any point $P$ of the rigid body can be seen as the ...
0
votes
2answers
44 views

Disk let free to rotate

A rigid body moving with no constraints, in particular rotating, will rotate necessarily about a principal axis of inertia. I thought that the reason of this is that otherwise, the angular momentum $\...
0
votes
1answer
49 views

Principal axes of inertia of a compound pendulum

I am confused about principal axes of inertia. Consider the compount pendulum in the picture, made of a rectangular plate. I oscillates about a horizontal axis $\hat{a}$ passing through $A$. The ...
0
votes
0answers
24 views

Distribution of contact force

Say we have a body resting on a flat surface. The force of gravity acts through the center of mass. The normal force is equal in size and in oposite direction. Since the body is in contact with ground,...
0
votes
0answers
17 views

Angular acceleration of rigid body due to a torque

For the rotation of a rigid body about a fixed axis $z$ the following holds. $$ \vec{τ_z}= \frac{d \vec{L_z}} {dt} =I_z \vec{α} \tag{1}$$ Where $ \vec{τ_z}$ is the component parallel to the axis $...
0
votes
1answer
36 views

Two bodies connected to each other with with a string of lenth L is a rigid body? [duplicate]

Suppose we have two bodies A and B, they are connected to each other with an ideal string of length $L$. Then is this system a rigid body? This system has 5 degrees of freedom ( 6-1 constraint). But a ...
0
votes
1answer
32 views

Instantaneous axis of rotation of a rigid body

For the description of rigid body motion, any point $O$ of the rigid body could be taken as reference, since the velocity of a generic point $P$ can be written in function of the angular velocity $\...
0
votes
2answers
30 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 ...
2
votes
2answers
61 views

Meaning of parallel axis theorem: why is the moment of inertia minimum if the axis passes through the CM?

From parallel axis theorem follows that, given a rigid body, the moment of inertia is minimum if calculated with respect to an axis passing through the center of mass. What is the physical meaning of ...
2
votes
1answer
34 views

Component of angular momentum perpendicular to the rotation axis in rigid body rotation

I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector $ \vec {L} $ which is perpendicular to the fixed axis of rotation $...
0
votes
1answer
33 views

Proof of constant angular velocity in rigid body motion

I'm studying rigid body motion on Landau but I'm having troubles to understand this proof of the fact that the angular velocity $\vec{\Omega}$ is constant for a rigid body. My doubt is about the ...
0
votes
0answers
55 views

Rigid body rotation about fixed axis with angular velocity not constant in magnitude

I'm trying to understand the properties of angular momentum in the rotation of a rigid body around a fixed axis $z$, when the angular momentum $\vec{L}$ is not parallel to the angular velocity $\vec{\...
2
votes
4answers
108 views

Is torque necessary in rigid body mechanics? [duplicate]

Suppose we have a weightless, rigid rod fixed at one end, but free to swing at the other, where there is a mass $m$ attached. If we want to determine the tangential acceleration of the mass using ...
1
vote
0answers
37 views

Torque on rotating rigid body and pivot point [duplicate]

Consider a rigid body performing a rotational motion around a vertical fixed axis $z$ with constant angular velocity $\vec{\Omega}$. The angular momentum vector $\vec{L}$ is not parallel to $z$ (and ...
1
vote
2answers
108 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 ...
1
vote
2answers
85 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 ...
1
vote
1answer
47 views

What is the relationship between $W_1$ and $W_2$? [closed]

I have a model which schematic is in the linked picture. Blue $A$ and $B$ are rotational joints, black and red shapes are rigid elements. $I_1$ is moment of inertia of black and red elements combined ...
0
votes
2answers
65 views

Does Angular Momentum change what I change Center Of Mass?

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
0
votes
1answer
51 views

Does the rotational form of Newton's second law always hold?

Does the equation, $$\vec \tau=I\vec \alpha$$ (rotational form of the second law) always hold? If not, in what conditions does it hold true?
3
votes
2answers
77 views

Why does a bowling ball hook in the shape of a parabola?

As an aspiring professional bowler, I'm attempting to understand all the factors that influence a bowling ball motion. The simplest case is when the bowling ball is a uniform sphere and the center of ...
1
vote
0answers
40 views

What causing the axis of rotation of a bowling ball to change

A bowler throw a bowling ball with an initial velocity and initial rotation. Let the initial velocity vector be parallel to the y-axis. Now, the ball is rotating about an axis, call that the axis of ...
1
vote
1answer
68 views

Rigid body motion degrees of freedom

A rigid body moving in $\mathbb{R^2}$ has 3 degrees of freedom and in $\mathbb{R^3}$ has 6 degrees of freedom. Could you please help me show that a rigid body moving in $\mathbb{R^n}$ has $\frac{n+n^2}...
0
votes
0answers
79 views

Why did Einstein allow unphysical objects in his 1906 paper on $E=mc^2$?

In the first part of this paper, Einstein considers a "rigid cylinder", "massless cavity", as well as a "massless carrier mechanism" that is used to transport the massless cavity. These hypothetical ...
0
votes
0answers
24 views

Relative velocity of the center of mass in a rotating coordinate system

Say I have a rigid body in space. Let k be a stationary coordinate system, K a coordinate system rotating together with the rigid body, so the transformation $B:k \rightarrow K$ it's just a simple ...
0
votes
1answer
35 views

Which force acts as centripetal force on gyroscope?

I think I have understood gyroscope in terms of angular momentum and how the torque of gravitational force moves it the way it does. Also I understand the direction in which it would move: What ...