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28 views

How many illusionary axes of rotation can coexist?

Consider the answer to this question: How many different axes of rotation can coexist? Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation. Now, that ...
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1answer
37 views

Does asymmetric rigid body experience torque-free precession?

I know that a top (or any axis symmetric body) experience torque-free precession. and I know that asymmetric body, with 3 different dimensions has stable rotation when the angular velocity is near the ...
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1answer
29 views

Why conserve angular momentum about COM

In many questions involving collisions between Rigid bodies angular momentum is conserved about center of mass If bodies stick together after collision they estimate com and then conserve about ...
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0answers
290 views

Newton's second law in angular form [duplicate]

I'm rather confused about the correct form of Newton's second law in angular form and how matrices of inertia could be converted from one coordinate system to the other. Consider the system below: ...
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2answers
50 views

Angular velocity of rotating rod

Consider the following system: Newton's second law for rotational motion: \begin{equation}\tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{...
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1answer
24 views

Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
1
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1answer
29 views

Angular Momentum and assymetric axis

The question I came across , If a semicircular disc rotates uniformly (const. angular velocity) about an axis passing through its Centre of mass , and prependicular to its plane , do we need an ...
1
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2answers
100 views

Mechanics: angular momentum of disk

I am studying mechanical engineering and I've got a problem with the angular momentum of objects that have a rotation which is rather complex to describe like the following: The shaft rotates around ...
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1answer
54 views

Torques in Euler equation

The Euler equation is given by $$\mathbf I\dot{\boldsymbol \omega}+\boldsymbol\omega\times \mathbf I\boldsymbol\omega= \mathbf M.$$ Also see here. It explains that The expressions for the torque in ...
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1answer
112 views

Integrating rigid body equations for a game engine simulation

I'm a mechanical engineer who's trying to implement a physics engine for a 3D game simulation, so I apologize for being incorrect or simply ignorant of some aspects of computation. I'm implementing ...
1
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1answer
50 views

In which scenarios is the derivative of mass moment of inertia ignored and taken into consideration for rigid bodies?

When taking the time derivative of Angular Momentum The first two terms represent the relative rate of change with respect to the coordinate system used. Most sources I have been reading state that ...
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1answer
866 views

Relation between acrobat and principle of conservation of angular momentum

How the principle of conservation of angular momentum is used by an acrobat to rotate a few revolution while leaping throung the air?
4
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0answers
353 views

Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
1
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1answer
264 views

Euler's equation for a rotating frame when the inertia tensor is non-diagonal

Wikipedia's entry for Euler's equation states: In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a ...
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0answers
67 views

Can angular momentum be affected by internal forces in a rigid body system?

This question is motivated by my interest in understanding the angular momentum and energy of a figure skater doing a stationary spin where they move their limbs away from and towards their body to ...
1
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1answer
456 views

Rotating Cone - Finding Energy and Momentum

I think I've a conceptual lacuna that needs to be filled, when it comes to a rigid body possessing angular velocities along more than one axes. Here's my doubt - Consider the following solid cone (...
9
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3answers
596 views

What is the physical meaning of the principal axes of inertia?

What is the physical meaning of the principal axes of inertia? I used to think that the axes of inertia are, in some sense, the only axes about which the body can rotate without the angular momentum "...
-1
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1answer
104 views

Rigid rotational dynamics problem [closed]

A thin uniform rod AB of mass $M$ and length $L$ is free to rotate in a vertical plane about a horizontal axle at end A. A piece of putty, also of mass $M$, is thrown with velocity $V$ horizontally at ...
5
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1answer
301 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 ...
1
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1answer
198 views

Why must the moment of inertia be a linear transformation?

It seems to be that in the context of rigid body dynamics, the moment of inertia is introduced as the quantity that maps the components of the angular velocity into the components of angular momentum. ...
2
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1answer
86 views

Why are the dynamics of $L_x$, $L_y$ not considered in case of a rigid body motion about $z$-axis?

Consider a non-planar rigid body rotating about a fixed axis (say, the Z-axis, chosen vertically). Let the origin $O$ is chosen somewhere on the Z-axis. Let $\textbf{r}_i$ represent the position ...
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2answers
843 views

Conservation of Angular Momentum about the point of collision

A uniform rod AC of length l and mass m is kept on a horizontal smooth plane. It is free to rotate and move. A particle of same mass m moving on the plane with velocity v strikes the rod at point B ...
2
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2answers
535 views

Conservation of angular momentum in Euler's equation

Consider the following equations \begin{align} I_1 \frac{dΩ_1}{dt} + (I_3 - I_2)Ω_2 Ω_3 &= K_1, \\ I_2 \frac{dΩ_2}{dt} + (I_1 - I_3)Ω_3 Ω_1 &= K_2, \\ I_3 \frac{dΩ_3}{dt} + (I_2 - I_1)Ω_1 Ω_2 ...
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1answer
124 views

Calculating time period of a rotating rigid body

I am given the following problem: A cuboid is rotating around the $AB$ axis at $t=0$, with no external forces acting on the cuboid. The lecturer question is: "When will the cuboid symmetry axis ...
2
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1answer
355 views

Euler equation and conservation of angular momentum (rigid body)

I am a beginner in this field. Just ask a simple question which confuses me. Please consider the following: Conservation of angular momentum about fixed point $o$: $\dot{H}_o = M$. $M$: the ...
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0answers
145 views

Elementary explanation for motion of a gyroscope [duplicate]

Gyroscope is a remarkable rigid body, and all the explanations that I have found, that describe its motion, are in terms of angular momentum and torque. An exception to it is the Feynman lectures on ...
1
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1answer
100 views

How to simplify the formula for the moment of inertia?

MOI can be defined as a tensor: $$ \mathbf{I} = \int(rr\mathbf{E} - \mathbf{r}\otimes\mathbf{r})dm $$ in this formula for angular momentum: $$ \mathbf{L} = \mathbf{I} \cdot \boldsymbol{\omega} $$ ...
2
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3answers
11k views

Hollow Cylinder vs Solid Cylinder [closed]

Thanks to angular momentum, we know that hollow cylinders are slower than solid cylinders when rolled down an inclined plane - Is this difference in speed (or time taken to get to the bottom of the ...
10
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2answers
365 views

Can a ball be struck to give it a spiral spin?

I play table tennis and we can hit balls to make them spin in pretty much every way possible except to spiral about its direction of travel like an American football throw. Of course it could be shot ...
46
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5answers
8k views

Why don't helicopters use reaction wheels to counter the main rotor?

As the main title says. I'm finding myself wondering about helicopters. The tail rotor is a vulnerable and key piece of equipment, especially on military helicopters. I know some helicopters instead ...
2
votes
1answer
196 views

Principal moment of inertia for a rotating body

My major is not in physics. I am reading the following paper: (my problem is simple and not related with any optimization) http://arxiv.org/abs/1410.2841 (p.5~p.6) Suppose The body ...
1
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2answers
91 views

Conceptual understanding behind moments of force for a rigid body cylinder

I have a question behind the conceptual understanding of the following equation: $$\frac{\text{d}}{\text{d}t}\mathbf{L}_G = \sum_i \ \mathbf{r}_i\times \mathbf{f}_i$$ where $\mathbf{L}_G$ is the total ...
1
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1answer
49 views

Finding the Mass of a Precessing Top

Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular ...
2
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1answer
638 views

Parallel axis theorem and Koenig theorem for angular momentum

Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics? The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$ Koenig theorem ...
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votes
1answer
1k views

Derivative of angular momentum of rigid body

I found this equation that describes the change in angular momentum $\vec{L}$ of a rigid body rotating about a fixed point $O$. $I_o$ is the moment of inertia of the body with respect to the axis of ...
0
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1answer
207 views

Calculation of support reaction in rigid body rotation and collisions

I can't understand the logic behind the calculation of torques exerted by supports in rigid body motion, especially rotation. The equation of angular momentum is $$\vec{\tau}=\frac{d\vec{L}}{dt}\tag{...
2
votes
1answer
504 views

Why is the center of mass frame always used in rigid body dynamics?

In most of the cases the center of mass is chosen for rigid body motion description, but this is not an obliged choice, since the motion of any point $P$ of the rigid body can be seen as the ...
0
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2answers
343 views

Disk let free to rotate

A rigid body moving with no constraints, in particular rotating, will rotate necessarily about a principal axis of inertia. I thought that the reason of this is that otherwise, the angular momentum $\...
0
votes
1answer
472 views

Principal axes of inertia of a compound pendulum

I am confused about principal axes of inertia. Consider the compount pendulum in the picture, made of a rectangular plate. I oscillates about a horizontal axis $\hat{a}$ passing through $A$. The ...
2
votes
1answer
474 views

Component of angular momentum perpendicular to the rotation axis in rigid body rotation

I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector $ \vec {L} $ which is perpendicular to the fixed axis of rotation $...
0
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0answers
53 views

Torque on rotating rigid body and pivot point [duplicate]

Consider a rigid body performing a rotational motion around a vertical fixed axis $z$ with constant angular velocity $\vec{\Omega}$. The angular momentum vector $\vec{L}$ is not parallel to $z$ (and ...
1
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2answers
446 views

Forces that exert torque on a rigid body in rotation when angular momentum is not parallel to angular velocity

I'm confused about the rotation of a rigid body, when the angular momentum $\vec{L}$ is not parallel to the angular velocity $\vec{\omega}$. Consider a barbell with two equal masses that rotates ...
1
vote
1answer
52 views

What is the relationship between $W_1$ and $W_2$? [closed]

I have a model which schematic is in the linked picture. Blue $A$ and $B$ are rotational joints, black and red shapes are rigid elements. $I_1$ is moment of inertia of black and red elements combined ...
-1
votes
3answers
700 views

Does angular momentum change what I change center of mass? [closed]

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
0
votes
1answer
495 views

Which force acts as centripetal force on gyroscope?

I think I have understood gyroscope in terms of angular momentum and how the torque of gravitational force moves it the way it does. Also I understand the direction in which it would move: What ...
0
votes
1answer
67 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
504 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 observed ...
2
votes
1answer
815 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.
2
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0answers
152 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 ...
3
votes
0answers
151 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 ...