# 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.

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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,...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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)
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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