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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69 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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Rolling motion of a solid hemisphere [closed]

A solid uniform hemisphere is placed vertically and released on a rough horizontal surface. It rolls without slipping to a horizontal position such that curved surface is touching the floor At this ...
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2answers
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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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0answers
27 views

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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0answers
55 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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1answer
27 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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2answers
74 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
44 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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0answers
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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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1answer
35 views

Can you explain gyroscopic precession using only Newton's three linear laws without applying their angular cousins?

Is there an intuitive approach to understand gyroscopic motion based on Newton's laws without passing through angular momentum conservation?
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1answer
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When do we have rigid body rotation in fluids?

I'm studying articles about spinning drop method. In most of approaches, the fluid movements are taken as rigid body rotation. My question is not about only spinning drop device, I want to know, when ...
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Simulating Rotor Blades for Quadcopter

I would like to simulate various shapes for rotor blades that will be used in a quadcopter. Which simulation software is used to understand how shapes, rotation interacts with the surrounding air? I ...
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1answer
81 views

Solving Rigid Body ODEs in rotating frame

I'm trying to solve numerically the motion of a rigid body in a fluid. To this end I have to solve the fluid PDEs, and at every time step the 6 ODEs of the rigid motion degrees of freedom: $$(m\...
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4answers
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Friction in case of pure rolling [closed]

I know that friction in pure rolling is zero.But in some questions friction is included such as on an inclined plane while in others friction is not included . I am very much confused with friction in ...
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1answer
43 views

Calculating Angular momentum of given problem [closed]

Question Attempt But by my method the answer comes out in terms of M ( mass of pulley) which not given. Where am I wrong? Also do provide alternate solution or suggestion. Please help.
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2answers
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Is the net torque of an only translating rigid body zero, independent of the point chosen?

I know that the Newton-Euler equations can be proven using the center of mass as reference, but I was wondering if this is a special case, or if you can provide a counter-example. We know that when a ...
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1answer
31 views

Forces in statically indeterminate system

I am a bit puzzled about the meaning of statically indeterminate in particular in terms of force distribution. The following system is clearly statically indeterminate: There are four reaction forces ...
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1answer
89 views

Is there any possibility to use the inertia tensor to express the Kinetic energy? [closed]

$$T=\frac{1}{2} \mathscr M \omega^2$$ Well in this situation the particle is in rotation. Can we express $T$ using the inertia tensor $I_{ij}$
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1answer
63 views

Why does the axis of spinning tops rotate about a vertical axis?

I have noticed that when we make a top spin, the top itself rotates about it's own axis and at the same time its axis of rotation will be moving in circles. How to explain this? Why can't it simply ...
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1answer
38 views

Still points in a rigid body

I'm reading Woodhouse's book on classical mechanics and I got stuck on this problem: A rigid body has angular velocity $\vec{\omega}$ and has one point $O$ fixed relative to a frame $\tilde{R}$. ...
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1answer
64 views

Moment of inertia of a body free to rotate

A square plate $ABCD$ of mass $m$ and side $a$ is suspended from point $A$ in vertical plane. A disc of the same mass and $\sqrt2a$ diameter is attached at point $C$ as shown in the figure. The disc ...
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1answer
92 views

How do you find the Triangle Inequality from an Inertia Matrix?

If you have an inertia matrix of the form $$\begin{pmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{yx} & I_{yy} & I_{yz} \\ I_{zx} & I_{zy} & I_{zz} \end{pmatrix}=I$$ If the matrix ...
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2answers
124 views

Point of application of pseudo-force?

Why do we take pseudo-force to pass through center of mass of a rigid body while calculating torque on the body using a non-inertial frame of reference? I was just told this fact in my class and ...
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2answers
70 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 ...
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5answers
126 views

Center of mass of constrained rigid body

Say we have a rod with center of mass at its geometric center. Rigid bodies rotate around center of mass. If you apply force $\mathbf{F}$ at distance $\mathbf{r}$ from center of mass you generate ...
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0answers
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Angular momentum conservation and multiple reference frames

So, i will start the topic with a very easy problem. At a first place I know the fact about the reaction torque that a body experiences when it has some kind of rotating parts (Lets say for example ...
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0answers
20 views

Ergodicity of free rigid body motion

Consider the (torque) free motion of a rigid body. This problem has 2 real parameters determining the relative magnitude of the principal moments of inertia. Is there any result that shows the motion ...
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4answers
99 views

Torque free rigid body

Is kinetic energy constant for a rigid body with one fixed point and no torque, if so how to prove it? I'm considering free rotation.
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1answer
76 views

Rotational Kinetic Energy of Rigid Bar

Consider a rigid bar (infinitely thin and with uniform mass density) of length $L$ with $x_1(t), x_2(t) \in \mathbb{R}^3$ each describing the positions of an endpoint of the bar in some fixed inertial ...
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0answers
31 views

Does gimbal for education exist?

I have been looking for a gimbal for a long time. Something similar to what you see in the book. However, I have had a lot of problem to find something similar. All my search results end to %95: ...
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1answer
35 views

What is the interplay between the “spinning tennis racket” effect on a planet with three principle axis of rotation and its moon?

Suppose I have a tennis racket spinning on its second axis of rotation such that it is subject to periodically flipping over on its spinning axis, as per the Dzhanibekov effect (explained in ...
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1answer
28 views

Rigid bodies: angular velocities, momentum, Inertia Tensor, rotational kinetic energy. Books suggestions?

I'm having a hard time with understanding how to model the rotational kinetic energy of rigid bodies. I will appreciate any good suggestion about resources such as books or videos regarding topics ...
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1answer
73 views

A subtlety about Lyapunov stability of stationary rotations of rigid body

On Page 145 of Arnold's mechanics book there is the intermediate axis theorem: "The stationary solutions of the Euler equations corresponding to the largest and smallest principal axes [of the ...
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1answer
32 views

A query on the solution of a gyroscope with friction

I have been trying to solve the motion of a gyroscope with friction added, so that as in reality, its spin will slow down with time. My first naive attempt to add friction has run into trouble and I ...
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0answers
30 views

Rigid body motion / rotation? [duplicate]

Let's say I have a 1 meter steel rod floating in the vacuum of deep space far from any significant gravitational force, and at rest relative to myself. Say I apply some force perpendicular to it and ...
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1answer
91 views

Finding the kinetic energy of a cylinder swinging inside another cylinder [closed]

I'd like to solve the following problem: An homogeneous cylinder of mass $m$, radius $a$ and height $h$ rolls without slipping inside a cylindrical surface of radius $R > a$. Find the kinetic ...
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1answer
77 views

Usefulness of rigid body dynamics in modern physics [closed]

Almost every great classical mechanics book has a huge chunk devoted to rigid body dynamics. For example, I'm going through Goldstein right now, and I'm anxious to get to Hamiltonian formalism and ...
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0answers
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How does a bottle spin? [closed]

I am preparing for my exam next monday and I decided to try and make some old exams. This is one exercise that i was not sure of. Assume a bottle is laying on an assembly line? (apologies for bad ...
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0answers
56 views

What minimum angular speed required for coin to spin on table? [closed]

When a coin is spinning on the table around the vertical axis passing its center, what is the minimum angular speed ($\omega$) is required to maintain this spinning? I would be thankful if you help ...
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0answers
9 views

Angular velocity in principle axis for free symmetrical top

I'm trying to analyze the free symmetrical top problem by calculating the Lagrangian in the principle axis system. but when I look in the books and try to understand how the kinetic energy was ...
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1answer
77 views

Conservation of Angular Momentum for Rigid Bodies

I have question about Conservation of Angular Momentum of Rigid Bodies. I've been doing some examples from Hibbeler's book, and noticed that in this chapter about Conservation of Angular Momentum of ...
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1answer
49 views

Torque due to a small block inside a cylinder on an inclined plane [closed]

If I have a small block inside a cylinder on a inclined plane. What is the torque on the cylinder due to the friction between the small block and the cylinder? It is easy if the center of the cylinder ...
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1answer
70 views

Is the motion of a spinning top chaotic?

When you spin a top, while it first wobbles, it will eventually reach a period when it spin 'smoothly', then finally falls to the ground. I'm curious about whether its motion (or maybe the path that a ...
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1answer
76 views

Gyroscope precession and Euler equations

I've been trying for so long to solve this problem, but the solution I have found isn't the one I expected. Basically, I have to solve Euler's equations for a gyroscope with a weigth at a distance d. ...
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3answers
255 views

An expert opinion on controversial video appearing to defy Newton's Laws [closed]

I really want another answer to this question than just my own. As many people probably know the late Prof Laithwaite in the UK (a brilliant electrical engineer) made the error of wandering outside ...
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1answer
44 views

Why can a gyroscope go upright for a while, after losing some energy?

There are many questions about gyroscopes, and this one: (Confusion about what happens when the rotating axis of a gyroscope is rotated) remind me of an odd behaviour of a toy gyroscope that I had. ...
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2answers
79 views

About the concept of Radius of gyration

According to Wikipedia: Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance of a point, from the axis of rotation at which, if whole mass of the ...
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3answers
70 views

Center of mass of a symmetrical rigid body

Suppose a rigid body has mirror symmetry along the $z$-Axis, i.e. $\rho(x,y,z)=\rho(-x,-y,z)$ where $\rho$ is the density of the body. How can I show from this that the center of mass lies on the $z$-...
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0answers
30 views

Measurements taken in Euler's equation of rigid body motion

I am having some confusion about the frames involved in Euler's equation of rotational motion. $$ \mathbf{I} \dot{\boldsymbol\omega} + \boldsymbol\omega \times \left( \mathbf{I} \boldsymbol\omega \...
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0answers
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Gyro mechanics with a coin [duplicate]

Take a coin and stick a little bit of chewing gum on it. Then give the coin some spin with your fingers. Why is the chewing gum moving to the top of the coin while it rotates? You could do also ...

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