# All Questions

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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 ...
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 ...
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 ...
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: ...
50 views

### Angular velocity of rotating rod

Consider the following system: Newton's second law for rotational motion: \tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
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....
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 ...
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 ...
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 (...
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 "...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: $$\mathbf{L} = \mathbf{I} \cdot \boldsymbol{\omega}$$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...