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

0
votes
1answer
40 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 ...
1
vote
1answer
65 views

How do I handle elastic contacts in a simulation with friction [closed]

I'm trying to simulate a wheel as it hits the ground. Problem 1 Suppose a disc is dropped from a height. It has initial velocity of $-x,-y$ caused by throwing and gravity. It has no initial angular ...
-1
votes
1answer
31 views

Understanding the constraint of tension with a rigid body

I want to know why doesn't $T_1 = T_2$? I think its probably because of the Pulley but still aren't the Tensions Equal but opposite in direction.
1
vote
1answer
102 views

Gyroscope precession

I have a system diagrammed and explained in the image below. Experimentally I believe the wheel will rotate around the pivot point where the cable is attached in a counter-clock motion if ...
1
vote
0answers
59 views

How can we solve 2D rigid body collision? [duplicate]

I know that usually collision with velocity collinear can be solved by simultaneous equations of both conservation of energy and linear momentum. But my question is when 2D velocity is encountered, we ...
0
votes
1answer
32 views

Why does this consider the center of mass instead of the end? (RIGID BODY MOTION) [closed]

A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end. The rod is released from rest in the horizontal position. What is its angular speed when it ...
0
votes
1answer
79 views

Angular momentum of a rigid body about any points

Is angular momentum about all points same if the body is rigid and is rotating/translating/rolling with a constant velocity? Why? No external force is acting on the body.
0
votes
1answer
48 views

Angular acceleration of a car door [closed]

http://imgur.com/F3eAF9F Edit: i uploaded to the site but it came out really blurry so heres the imgur link I don't get the solution at all, where does the -ma r cos theta come from? (Sorry on my ...
3
votes
4answers
137 views

Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
0
votes
0answers
45 views

Tangential Velocity of a Rotating Rod

I have the following question which has given rise to a doubt. Question: 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 ...
0
votes
1answer
73 views

Why do we need theorems like **Parallel Axis Theorem**

In rigid body pure rotation, quantities like $\omega, \tau, L, I, r_i$ (symbol with usual meaning) are axis dependent. Assume rigid body to be sphere rotating about the axis passing trough the center. ...
0
votes
0answers
45 views

What is required for a time-varying moment of inertia matrix?

Let me preface this question by stating that I am familiar with euler's equations for rigid body dynamics, torque and angular momentum. Despite the math, I'm still a little fuzzy about certain ...
0
votes
0answers
21 views

Equation of motion for rigid T-shaped object

Suppose I have a rigid T-shaped object, that is described by three points $A,B$ and $C$. $A$ and $B$ describe the corners of the "top" of the "T", lets say these have coordinates in 3D of $r_A = ...
2
votes
0answers
72 views

Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
0
votes
1answer
71 views

How to set up the Lagrangian for this kind of problem?

I'm currently studying rigid bodies in Goldstein's Classical Mechanics book but although I understand the theory I'm not yet understanding how to set up the Lagrangian in some situations. One such ...
3
votes
0answers
90 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
0
votes
0answers
22 views

Polygon with moving/rotating vertices (or chained line segments)

Suppose we have a polygon, where vertices are point masses, and rods joining them are massless. Now, we pull one of the vertices, what equations govern the motion. How about if instead of a polygon we ...
6
votes
1answer
273 views

Intuitive Explanation of Tippe Top Effect?

A friend showed me a tippe top (a special kind of spinning top) lately and asked me about the physics behind it. I thought about it for a while but cannot quite figure it out. So I will throw the ...
0
votes
1answer
36 views

Formula for speed of rigidly connected objects with one “turning off” of the line?

In the diagram below I have two objects traveling up the diagram on the black track at some speed s, separated by distance D connected by a breakable rigid rod. Further along the straight-line track, ...
1
vote
2answers
78 views

Configuration manifold of a rigid body

As I know, a rigid body is a set of $N$ particles in three-dimensional space subject to the following constraint: if $b_1,\dots,b_N\in \mathbb{R}^3$ are the initial positions of the particles and if ...
0
votes
0answers
26 views

Rotational Velocity

I would like to calculate rotational velocity from Global(fixed frame of reference) in local (moving frame of reference). How to do that? i know the relationship between global and local frame of ...
5
votes
2answers
445 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 ...
2
votes
1answer
52 views

Will a coin topple if the center of the coin is just on the corner of the square table?

3/4th of the coin is outside the table and 1/4th is on the inside. Also assume that the center of the coin is just on the inside.
0
votes
1answer
40 views

How does axial offset effect rotor balance?

I have a thin rod rotating about its primary axis, rigidly attached to mass $m_1$ whose center sits at distance $r_1$ from the axis and position $y_1$ along the axis. $m_1$ exerts a centripetal force ...
0
votes
2answers
74 views

Rod partially handing off edge of table

A uniform rigid rod of length $L$ lies at the edge of a frictionless table so length $x$ of the rod rests on the table and the rest is beyond its edge. Intuition suggests that the rod will stay like ...
0
votes
1answer
75 views

Transform velocities from one frame to an other within a rigid body

I come from non-physics background but just came to face the following problem. I have a rigid body with two attached frames of reference A and A'. I know: the rotation and translation between A ...
1
vote
1answer
88 views

When we ride a bicycle, why do we tend to move left when we turn it right? [duplicate]

When we ride a bicycle, we tend to move our body left if we are taking a right turn and vice versa. Why is it like that?
6
votes
0answers
64 views

Why is this handle flipping back and forth? [duplicate]

This gif of some kind of handle being spun in zero gravity has been doing the rounds: Why is it flipping back and forth? It seems odd that it flips, then seems to rotate around one axis in a ...
1
vote
0answers
80 views

Rotational dynamics equation for a variable mass system?

I'm searching for the formulation of Euler's rigid body dynamics in the case of a variable mass system. I'm reading the book Mechanics of Flight by Warren F. Phillips (2nd edition) and unfortunately ...
2
votes
1answer
176 views

Kinematics of Euler angles relative to a rotating frame

I have a rotating body $B$ and a rotating frame $F$ whose orientations are described by the quaternions $q_B$ and $q_F$ respectively. I also have the angular velocity vectors $\omega_B$ and ...
1
vote
1answer
50 views

'Eulerian' description of a rigid body submerged in fluid

In this paper, equations of rigid body motion (eq 4 and 5 in the paper) are written in Eulerian form (eq 12 in the paper). The rigid body is submerged in a viscous incompressible fluid. ...
3
votes
1answer
87 views

Equation of Motion for Rigid Body Motion

In a paper, eq 24 I am reading, the author mentions the equation of rigid body motion which is written as the sum of translational motion of the centre of mass, $x_G(t)$ and a rotational term about an ...
1
vote
2answers
129 views

Force of an ideal spring

Suppose you have an ideal spring (constant of the spring $k$) attached to a uniform disc of radius $R$ as in the picture below: The force $F$ in red is from the spring. My question is the ...
2
votes
2answers
133 views

Are Fluted Barrels More Rigid Than Standard Ones?

This seems to be quite a debated topic in the shooting community and is something I'm not sure about. A fluted barrel is a barrel that has grooves milled into it to reduce weight, help it cool faster ...
5
votes
3answers
2k views

Paradox in the two block problem [closed]

UPDATE (regarding duplicate) : This question is not a duplicate of another question. Sure, the situation in both the questions is same and, yes, both questions ultimately provide a methodology to ...
1
vote
1answer
185 views

How far does a ball thrown over a surface with friction slide until it starts rotating? [closed]

A bowling ball is thrown horizontally with initial velocity $v$ and no initial rotation over a surface with static coefficient of friction $\mu$. Determine the distance the ball travels ($d$) until ...
7
votes
4answers
393 views

How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
1
vote
1answer
126 views

Angular acceleration as a function of torque

I know that the angular momentum $\mathbf{L}_{cm}$ with respect to the centre of mass of a rigid body can be expressed as $I\boldsymbol{\omega}$ where $I$ is the inertia matrix and ...
3
votes
2answers
1k views

Angular momentum with respect to the centre of mass

I have been told [Warning: I leave this because it's what I asked and allows to understand the dialogues in the comments, but Azad, whom I thank, has pointed that the formula does not hold in general ...
2
votes
1answer
67 views

Analysis of motion of a body moving on a string?

I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ...
0
votes
1answer
76 views

Why does plugging a hole in an airplane's fuselage result in a huge (10x) atmospheric pressure spike?

While reading about uncontrolled decompression, I came across one famous airline incident, Aloha Airlines Flight 243, where the article I was reading discussed a 1-square-foot hole created in the ...
0
votes
1answer
14 views

What is the potential associated to a pure torque proportional to one of the principal axis of a particle?

I'm writing a code in molecular dynamics in which a particle is subject to a pure torque around one of its principal axis. E.g., if the particle has principle axis $\hat u$, $\hat v$, $\hat f$, all ...
0
votes
1answer
118 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 ...
1
vote
1answer
638 views

Approximating the moment of inertia of a quadcopter [closed]

I want to compute an approximated moment of inertia for my quadcopter: my idea is to take the frame and the electronics, approximate it as a sphere in the center of mass $M$ and radius $R$ (with ...
3
votes
1answer
250 views

Tensor components change under rotation-translation

I am currently working on a research project in a non-physics field, where I would like to work on a very constrained 2nd order tensor (3x3, symmetric, traceless). The tensor represents probability of ...
19
votes
12answers
5k views

How can the contact point of rolling body 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?
3
votes
1answer
1k views

Equation of motion for the center of mass of a rigid body

The center of mass of a rigid body is given by: $$ \vec{r}_c = \frac{1}{M} \sum_i m_i \cdot \vec{r}_i $$ with $M = \sum_i m_i$ the total mass or $$ \vec{r}_c = \frac{1}{M} \int \vec{r}\ ' \cdot ...
2
votes
2answers
160 views

Torque on puck moving on plane without friction

We have two pucks moving on a plane without friction. On one of them a force is applied on it's center of mass. On the second a force of equal magnitude is acting tangential to the puck and at a ...
0
votes
0answers
44 views

A free axis of rotation [duplicate]

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
2
votes
2answers
255 views

Reaction to gyroscopic force [duplicate]

Just like the reaction of the weight of a body is a force acting on Earth towards the body, where and in what direction does the reaction of a gyroscopic force act?