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.
884
questions
6
votes
4
answers
298
views
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 ...
- 1,135
6
votes
1
answer
3k
views
Can any physical rigid body be represented by an ellipsoid with the same angular dynamics?
According to wikipedia, the inertia tensor of an ellipsoid with semi-axes $a,b,c$ and mass $m$ is
$$\left[\begin{array}{ccc}
\frac{m}{5}(b^2+c^2)&0&0\\
0&\frac{m}{5}(a^2+c^2)&0\\
0&...
- 355
6
votes
1
answer
2k
views
A Question about Virtual Work related to Newton's Third Law
In describing d'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as,
$$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$
where $...
- 170
6
votes
1
answer
412
views
The greatest rotation inertia of a system?
Consider this scenario: There are $n$ tiny balls (tiny means we can fix several balls in one place) with mass $m_1,m_2,...$ fixed in a stick which we may ignore the mass of the stick. Now we rotate ...
- 111
6
votes
2
answers
3k
views
Consider a horizontal surface with or without friction. Ideally, will a wheel rolling without slipping roll forever in both cases?
Suppose a wheel is rolling smoothly on a horizontal plane i.e., it is rolling without slipping.
Now let's take the two cases of the horizontal plane:
It has friction
It is frictionless
In the first ...
- 265
6
votes
1
answer
2k
views
Euler's equations of rigid body motion from least action principle
I would like to derive Euler's equations of rigid body motion from least action principle.
Suppose we are in free space so we have no gravity so Lagrangian is equal to kinetic energy.
$$
L = T = \...
- 728
6
votes
1
answer
340
views
Is there a "most unstable rigid body shape" when spun about its intermediate axis?
Is there a shape of a solid, that provides the quickest and most violent deviation of its axis of rotation, when spun around its intermediate axis? What would be this shape and does it depend on a ...
- 171
6
votes
4
answers
4k
views
Is there a formula for the rotation vector in terms of the angular velocity vector?
Euler's theorem of rotations states that for any rigid body motion with one point fixed is equivalent to a rotation about some axis passing through that fixed point. So let's consider a rigid body ...
- 2,902
6
votes
1
answer
166
views
How to numerically simulate a rolling object? [closed]
I am a maths person and definitely not a physics person, so maybe this is taught somewhere and I haven't learned it. I am trying to understand and figure out how to simulate rolling an object on a ...
- 171
6
votes
1
answer
1k
views
How do we prove the existence of the instantaneous axis of rotation?
Euler's theorem of rotation states that any rigid body motion with one point fixed is equivalent to a rotation about some axis passing through that fixed point. Now it is often said that Euler's ...
- 2,902
6
votes
5
answers
448
views
General plane motion and freely floating rigid body
Consider a rigid rectangular plate of length $l$, width $w$ and thickness $t$ which is at rest and is floating freely in space (no gravity). The center of the plate is at $O_L$ with respect to global ...
6
votes
2
answers
211
views
Rigid body object - translative and rotational forces?
If I have free 2D rigid body with 3 point masses, m1, m2 and m3, and I have 3 forces F1, F2 and F3 acting on these three masses, is it correct to say that the net translative force on the Centre of ...
- 61
6
votes
0
answers
102
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 ...
- 161
5
votes
4
answers
706
views
Why does a smooth rolling ball roll indefinitely despite there being static friction? [duplicate]
For a rigid smooth rolling ball rolling down a ramp (as seen above), the acceleration of the center of mass is given by:
$$a_{\text{com}, x} = - \frac{g \sin θ}{1+\frac{I_\text{com}}{MR^2}}.$$
However,...
- 53
5
votes
1
answer
470
views
Rigid body rotation apparent energy paradox
I'm doing some calculations on the motion of a rigid body as part of a project, and (as a tangent) I've come across something that I can't quite explain.
Case 1: If I apply a force $F$ though the ...
- 163
5
votes
7
answers
560
views
Is work done by torque due to friction in pure rolling?
This question has been asked and answered numerous times. I went through almost all of them and found no consensus. I found that all of the answers can be divided into two categories:
Friction does ...
- 1,002
5
votes
3
answers
879
views
Do Newton's laws of motion apply on rigid bodies?
If they apply on rigid bodies, would we consider forces acting in any direction or on any part of the body, and consider only the centre of mass when we talk about its momentum or the body being at ...
- 51
5
votes
2
answers
1k
views
Rigid body dynamics derivation from Newton's laws for higher dimensions
Since Newton's laws are defined for point particles, I'd like to derive some laws of motions for rigid bodies only by considering a rigid body as a system of particles such that the distances from ...
- 185
5
votes
2
answers
1k
views
Why can any general motion of a rigid body be represented as translation + rotation about center of mass?
Why can any general motion of a rigid body be represented as translation + rotation about center of mass?
I am beginning to read rotational dynamics and my textbook states this fact without proof. I ...
- 107
5
votes
2
answers
21k
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 ...
5
votes
2
answers
6k
views
Combining Moment of Inertia Tensors
In a physics simulation of rigid bodies, if I have a cube with a known mass and moment of inertia tensor, and I attach it to another cube with a known mass and moment of inertia tensor such that its ...
- 277
5
votes
2
answers
448
views
When two systems of forces acting on a rigid body are equivalent?
My book says that "it is clear that if you replace the system of forces with a second system having the same resulting force and the same resulting moment, with the same initial conditions the ...
user291161
5
votes
2
answers
901
views
Moment of inertia meaning?
Why is the formula for calculating the moment of inertia this integral
$$
\int r^2 dm~?
$$
I understand the way we derived this formula from looking at the distribution of kinetic energy of a ...
- 357
5
votes
2
answers
11k
views
Representation Of Linear Velocity as Cross Product
Why is linear velocity represented as cross product of angular velocity of the particle and its position vector? Why not vice versa?
(Consider rigid body rotation)
user74370
5
votes
1
answer
1k
views
How to simulate rotational instability?
I'm trying to simulate (for an educational game) the well-known effect that rotating objects with three nonequal moments of inertia are unstable when rotated around the middle axis.
Some explanations ...
- 241
5
votes
1
answer
7k
views
Elastic collision of rotating bodies
How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics?
I'm writing simple physics engine, but now only simulating non-...
- 257
5
votes
2
answers
6k
views
Deriving torque from Euler-Lagrange equation
How could you derive an equation for the torque on a rotating (but not translating) rigid body from the Euler-Lagrange equation? As far as I know from my first class in Classical Mechanics, there is ...
- 51
5
votes
4
answers
337
views
Does the intermediate axis theorem violate angular momentum conservation?
According to the intermediate axis theorem, an object rotating about its intermediate axis with a very slight perturbation will undergo periodic flips in its orientation in the absence of external ...
- 63
5
votes
2
answers
2k
views
What happens when I roll a gyroscope along its axis of spin?
Say:
I have a gyroscope that is spinning in the xy plane along the z axis.
I then roll its spinning axis by some angle theta
Now I know the gyroscope will resist my attempting to change its axis of ...
- 151
5
votes
2
answers
541
views
What's the difference between classical rigidity and Born-rigidity?
In classical mechanics, you have the concept of a rigid body. This notion is incompatible with the theory of special relativity.
In 1909, Max Born introduced the concept of Born-rigidity. He did this ...
5
votes
2
answers
2k
views
Rigid body dynamics joints
I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
- 151
5
votes
1
answer
583
views
Choosing principal axes for symmetric top
I am following Landau. Here $\mathbf{L}$ is angular momentum and $\mathbf{\Omega}$ is the angular velocity. The qualitative treatment for symmetric top in absence of gravity starts by choosing ...
- 174
5
votes
1
answer
1k
views
Why doesn't the 9th ball move in the break in the nine-ball pool game?
In the game of nine-ball pool, we break the rack
like shown below:
In the break, we hit the 1st ball with the cue ball. Many people familiar with pool games say that if the rack is constructed ...
5
votes
5
answers
2k
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 $OA$.
...
- 227
4
votes
7
answers
2k
views
When we say a rigid body is a system of particles, what exactly are 'particles' here?
In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have ...
- 501
4
votes
4
answers
2k
views
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 ...
- 175
4
votes
2
answers
1k
views
Why do we talk about inertia tensor?
When we talk about the inertia of a rigid body, in calculating the angular momentum as a function of the moment of inertia and angular velocity, the inertia tensor is introduced. But why is it a ...
- 911
4
votes
2
answers
859
views
Rigid body motion decomposition
A rigid body motion can be decomposed into translation and rotation. My question is, given a rigid body motion velocities of all points in the body, how to decompose this velocity field into a ...
- 153
4
votes
4
answers
464
views
How can a rigid body's weight do work on it to make it rotate?
Consider a cylinder that rolls without sliding on an inclined plane. If it's placed at the top of the plane, with its center of mass at a height $h$ from the bottom, it will have a potential energy $...
- 51
4
votes
3
answers
2k
views
Physical meaning of the moment of inertia about an axis
In the context of rigid bodies, the inertia tensor is defined as the linear map that takes angular velocity to angular momentum, that is, the linear map $I : \mathbb{R}^3\to \mathbb{R}^3$ such that
$$...
- 34.2k
4
votes
2
answers
6k
views
degree of freedom of a rigid body 5 or 6?
I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation.
But we have only ...
- 185
4
votes
5
answers
3k
views
Adding forces acting at different points on a body
Is it possible to vectorially add and find the resultant of several forces acting on different points of an extended body? For example, if I apply a couple (equal and opposite forces) to the two ends ...
- 25.5k
4
votes
4
answers
6k
views
What make the bottom portion of a wheel in rolling motion move?
As I just learn about the rolling motion which is the combination of pure translation and pure rotation. The top portion of the rolling body has the speed of double speed at the center of the object ...
- 661
4
votes
3
answers
228
views
Kinetic energy in combined rotational and translational motion
If a body is free to move I have studied that any point can be assumed to be in translational motion with velocity of the centre of mass along with a pure rotational motion with $\omega$. For Kinetic ...
- 71
4
votes
2
answers
565
views
What is the angular momentum of a particle rotating around an axis in 3D?
What would be the angular momentum of the particle at position $r_i$ in the diagram above?
The vector from the axis of rotation is $R_i$ and the tangential velocity is $v_i$ so the magnitude of ...
- 313
4
votes
1
answer
9k
views
Equation of motion for the center of mass of a rigid body
The center of mass of a rigid body is given by:
$$ \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 \...
- 3,056
4
votes
3
answers
305
views
Energy Conservation in Rolling without Slipping Scenario [closed]
A solid ball with mass $M$ and radius $R$ is placed on a table and given a sharp impulse so that its center of mass initially moves with velocity $v_o$, with no rolling. The ball has a friction ...
4
votes
1
answer
2k
views
How come a rigid body has 6 degrees of freedoms (DOFs) ? Isn't velocity a DOF?
For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?
4
votes
2
answers
175
views
Degrees of freedom of constrained rigid body
A rigid body constrained at a distance $r$ from its center of mass with a ball-and-socket type constraint is considered to only have three (rotational) degrees of freedom. But isn't rigid body's ...
- 187
4
votes
2
answers
1k
views
Angular Momentum of a rigid, extended object: When we see a rotating object, is the state of rotation totally relative?
Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum.
It is often said that an object that has been thrown up in the air ...
- 131