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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21 views

Determining the principal moment(s) of inertia and KE of a cuboid

I am a bit perplexed with regards rotations about a certain axis. Say we have a cuboid with lengths $l_1$, $l_2$, $l_3$ (not a cube, so $l_1$ does not equal $l_2$ does not equal $l_3$). I am okay with ...
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15 views

Pitch in Screw Motion of Rigid Body

Does anyone know how to prove these statements?
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Rigidity Vs. Viscosity and Bulk modulus

Can one consider a rigid body as a fluid having infinite viscosity and bulk modulus? Basically, I am asking if is it possible to start from Navier-Stokes equations (including Bulk modulus and ...
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35 views

Does a rotating rigid ring (or other rotating rigid body) in space generate heat?

I don't have training in physics (so forgive me if I use the wrong terms or mix up concepts), but I was thinking about “artificial gravity” in space. If a spaceship were being propelled by some force, ...
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Is there a quantum analogue of the “Tennis Racket” theorem?

A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is ...
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35 views

Applying forces to move spaceship without torque

I'm building a game prototype where you control a 2D spaceship by activating it's thrusters. Below is an schema of my thruster. It applies a force in the direction of the arrow, with a variable and ...
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3answers
63 views

Why is the vibrational kinetic energy of a body ignored when calculating the total kinetic energy?

In calculating the total kinetic energy of a macroscopic rigid body, we add the total translational kinetic energy and the total rotational kinetic energy of the constituent particles. Why is the ...
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77 views

A problem on Degrees of Freedom

Degrees of freedom of a massless rod, moving freely in space with a speck which is constrained to move on it? It seems massless rod is ideal I am very confused how to regulate degrees of freedom. ...
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78 views

If the net external moment on a body about a point is zero

I was told that If net external moment of some forces is zero about a point, then the net external force passes through the point. I know it's not true in general, what was the special condition ...
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35 views

Relating angular velocity between rotating frames

Notation I'll be using Hubert Hahn's notation for my question. Hahn has an algebraic treatment of all values. $\omega_{GN}^{G}$ is the angular velocity of frame $G$ with respect to frame $N$, ...
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79 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 ...
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Physical meaning of product of inertia [duplicate]

I'm trying to intuitively get this concept. Conventionally, $I_{xz}$ for example, signifies the $x$ component of $L$, the angular momentum, when $\omega$, the angular velocity, is in the $z$ direction....
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Are the ideas of angular velocity, angular acceleration, angular momentum, torque, etc only helpful for rigid bodies?

For rigid bodies, all the particles can have different linear velocities but the same angular velocity, so it makes it convenient to talk about the angular velocity instead. From there, we get to ...
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42 views

Clarification regarding Principal axes in rigid-body motion

Question: We need to find, the angular momentum of the assembly, about the Center of mass. As per Kleppner and Kolenkow, the general Expression for $\vec{L}$ about any point is: $$\vec{L_{p}}=I_1\vec\...
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How can different points on a rigid body move with different speeds but also be relatively at rest?

For a rigid body rotating with a constant angular speed, the points near the axis must have lower linear velocity than the points farther away. If they have different linear velocities, they must have ...
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Why does the motion of the center of mass model the motion of the entire system of particles?

A theorem in my physics textbook says: The overall translational motion of a system of particles can be analyzed using Newton’s laws as if all the mass were concentrated at the center of mass and the ...
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Books for advanced rigid body mechanics [duplicate]

I’m an undergrad Interested in rigid body mechanics. I’ve already covered the material on kleppner’s book as well as Goldstein’s and I’m still doing some problems from Morin’s. I want to know where to ...
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49 views

Precession of Angular momentum of Symmetric Top

For a torque free symmetric top, is the angular momentum in body fixed coordinates in same direction as instantaneous axis of rotation? I know that instantaneous axis of rotation precesses about ...
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1answer
21 views

Mathematical Derivation of the Condition of Equilibrium of a Rigid Body

We know that for a body to be in equilibrium, the resultant force and resultant torque must be both zero. The question is: can we derive this from more fundamental principles mathematically, such as ...
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2answers
44 views

Could anyone provide me with derivation for planar moment of inertia? I also have a couple of aditional doubts [closed]

I've been searching for the derivation of planar moment of inertial but I can't find it anywhere $(I = \iint y^2dA)$. I don't understand why there's a $y^2$ term in there but I do understand that you ...
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63 views

Confusion about relation between inertial an non-inertial reference frames in respect tto the motion of a rigid body

In "Analytical Mechanics" by N. A. Lemos, in page 99 the author determines the time derivative relation between an inertial frame $\Sigma$ an an non-inertial frame $\Sigma'$ fixed in a ...
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3answers
133 views

Intuition behind the center of mass

I know how the center of mass is defined, mathematically. It is the mass weighted average position of all the particles of a system. But calculating centers of mass and solving kinematic and dynamics ...
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2answers
118 views

Force required to Stop a Cone made by Paper from Flattening Out

Suppose a paper cone is made with height equal to its radius, only the two straight sides just touch each other and are not glued together. It is kept on a frictionless table and a vertical force is ...
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2answers
128 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 ...
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1answer
69 views

Is this book correct?

I'm currently reading this book on flight dynamics but I'm having some trouble getting my head around the way the author derives some equations of motion. He starts by showing the body in the first ...
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91 views

What will be the radius of the circle of the rolling coin? Gyroscope task [closed]

I try to calculate the radius of the rolling coin. The task was found in physics book https://www.amazon.co.uk/General-Course-Physics-1-Mechanics/dp/5922102257 (only in Russian). But unfortunately my ...
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1answer
47 views

Equation of motion for rigid body dynamics with quaternions

I'm trying to understand the equation of motion for rigid body dynamics in the presence of a quaternion joint for the root of a humanoid robot. But the dimensionality inconsistency issue is confusing ...
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3answers
105 views

Computing velocity and rotation of rigid body after application of force

Suppose we have a rigid body (or even a collection of point masses connected via rigid rods). Suppose this body is floating in space. Suppose we apply a force on this body over a duration of time and ...
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1answer
73 views

Special Relativity - World Lines (for rigid bodies) [closed]

S is an inertial reference frame with origin at O. A unit rigid* rod AB is at rest with respect to S. A and B are end-points of the rod. $xA=0$ and $xB=1$ At $t=1$, point A start accelerating ...
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72 views

Physical interpretation of the definition of angular momentum in classical mechanics

To what I understand, the following is a valid way to introduce the angular momentum $\mathbf L$ in the Lagrangian system of a rigid body. We can consider the extended configuration space to be $M\...
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4answers
47 views

Direction of friction of a rotating ring/disk

I'm trying to understand friction but I'm getting a bit confused... If I have a ring rotating on the ground around its COM what is the direction of the friction? If I have the same ring, but this time ...
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21 views

Equilibrium Reaction Forces on an Inclined Rod

Suppose we have a uniform steel rod leaning against a friction less wall in static equilibrium. Frictional force between the lower end and the floor is less than its limiting value by a finite amount. ...
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9 views

How exactly does a control moment gyroscope work?

I've searched a lot, but have not been able to find a proper explanation for the working of a control moment gyroscope. Could someone please explain it to me, preferably with vectors?
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1answer
90 views

Is there an egg that rolls infinitely far with no starting momentum?

This occurred to me when making an omelet. I want to construct a 3-dimensional rigid egg that when placed stationary on a flat surface with no friction or slipping either rolls to an unbounded ...
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1answer
13 views

Reducing the line of collision of two rigidbodies while using the coefficient of restitution

I am trying to solve the problem of the collision of any two rigid-bodies. So far this is what I got: I am concerned with the part where I reduce the equation with the coefficient of restitution by $\...
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1answer
38 views

How to obtain the variational of a vector (velocity vector)?

I recently started to study flight dynamics and I have to derive the equations of motion of a plane from the Hamilton's Principle. To better understand this principle, it is needed to have some ...
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2answers
48 views

When does the Newton's second law for progressive motion apply to a rigid-body and why? [closed]

Disclaimer: I may seem to be using strange terms because although I know English rather well, it is not the language I learn physics in. Consider a cylinder (with mass $m$ and radius $r$) on an ...
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1answer
35 views

Conserved quantities for the system consisting of an uniform spinning top

A uniform top of mass $M$ with its lower end fixed to the ground is rotating on its axis of symmetry with angular velocity $\Omega$, initially in a vertical position ($\theta=0, \dot \theta=0$). The ...
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1answer
77 views

Why is total kinetic energy always equal to the sum of rotational and translational kinetic energies?

My derivation is as follows. The total KE, $T_r$ for a rigid object purely rotating about an axis with angular velocity $w$ and with the i'th particle rotating with velocity $ v_{(rot)i} = r_i \times{...
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71 views

Proving that the angular velocity of a rigid body is the same about any point

Please consider the below image which is from Rana and Joag, Classical Mechanics. They build on a proof, which I reiterate below and through it they show that angular velocity of any point B in the ...
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1answer
39 views

Work done on rigid body vs particle

I know that the basic definition of the work done on a particle is: $$W_{12}=\int_1^2\mathbf{F}\cdot\mathrm{d}\mathbf{r}$$ but what if I have want to calculate the work done on a rigid body? is the ...
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Confusion regarding configuration space of a rigid body as described in Theodore Frankel

Assume a rigid body has one point, the origin of $\mathrm{R}^3$, fixed. By comparing a cartesian right-handed system fixed in the body with that of $\mathrm{R}^3$ we see that the configuration of the ...
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86 views

How can all particles of a rigid body have identical angular velocity when their position vector is not perpendicular to the axis?

Consider this spinning disk, in a 3D coordinate system. It is translated above the origin of the coordinate system and spinning around the axis given by this translation vector. Every source I can ...
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70 views

Derivation of $\frac{d}{dt}\mathbf L = I \dot{\boldsymbol \omega} = \mathbf M - \boldsymbol \omega \times \mathbf L$

I would like to know how the above quantity is derived (Here $\mathbf{M}$ is the rate of change of angular momentum with respect to a non inertial frame).I tried looking at various sources and couldn'...
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Acceleration of a merry-go-around, when a human is walking along it's rim

According to law of conservation of angular momentum, the merry-go-around is expected to rotate at constant angular velocity, while the man walks along it's rim with constant speed relatively to the ...
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59 views

Generalized coordinates of two unequal masses attached to a mass-less rigid rod

Consider a system of two particles of masses $m_1$ and $m_2$ moving in a plane. Let the respective position vectors be $\mathbf{r_1}$ and $\mathbf{r_2}$. The particles are attached at the end of a ...
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32 views

What is the moment acceleration of the center of mass for a rigid body under an external force

As shown in the following, a rigid body experiences an external force $\overrightarrow{F}$ away from its center of mass C: The rigid body is assumed to be free in space, experiencing no other force. ...
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81 views

Can someone please explain Gyroscopic precession?

So I watched this video It is a fairly popular one by veritasium, and one that confused me. I was wondering if someone can cover the physics behind this in a intutitive and easy to understand manner. ...
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1answer
51 views

Understanding the internal forces in rigid body motion

Suppose I consider a massless rod of several discrete masses with an external force being applied to one of the masses. Following the derivation here, the net torque on the system depends only on the ...
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Changing axis of rotation?

Let's say I've got a massless rod, at the end of which, I've attached 2 identical balls. Now say I drop the rod, such that it collides with the ground and for some reason, the coefficient of ...

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