# Tagged Questions

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### Planar motion in central forces

In a two body problem under central force, corresponding to a potential $V(r)$(assume one body is massive compared to the other so that its motion is negligible), conservation of angular momentum ...
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### Does mass equal angular momentum?

At the wikipedia pages for angular momentum ($L$) and moment of inertia ($I$) we find the equations: $$L=I \omega$$ $$I=m r^2$$ where $m$ is mass and $r$ is the distance between said mass and ...
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### Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...
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### Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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### Angular momentum conservation in a central field through the Hamiltonian

In my teacher's notes there is a discussion of the Hamiltonian for a central force field with potential $V(r)$. The Hamiltonian is formulated in spherical polar coordinates: ...
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### Angular momentum components as independent integrals of motion

I was told that in order to solve the Kepler problem (6 degrees of freedom in total) you have to proceed, step by step, to reduce those degrees of freedom using the integrals of motion. You do so ...
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### Rotationally invariant body and principal axis

Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$). Is it true that in this case the ...
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### Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, ...
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### Conservation of angular momentum in helicopter

I have a small RC-controlled toy helicopter with removable tail rotor. Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...
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### Will a precessing spinning wheel fall down if there is no friction at all?

If there where no friction at all, would a spinning wheel held up by one end of the axis spin precess forever without falling down? I just asked another question about the same problem: Direction ...
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### Direction of torque precession of a spinning wheel

Consider a spinning wheel, which is held up by one end of it's axis like this: To explain why the change of angular momentum is directed as shown in the figure above, one usually says that there is ...
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### Why do control moment gyroscopes exhibit “torque amplification”?

There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
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### Spin angular momentum of a system of particles : Is there any energy associated with it?

Consider a system of point particles , where the mass of particle $i$ is $Î¼_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the ...
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### Converting angular velocity to linear velocity through friction

A very basic question here; it's related to this one, but not quite the same. If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r$ and inertial tensor $I$ has ...
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### Effect of rotation on turbulence threshold for Reynolds number?

If the significance of the Reynolds number is: Then what is the effect of angular momentum on the transition from laminar to turbulent as in a convective vortex? Waterspouts, in particular, seem ...
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### How is angular momentum conserved when a spinning top finally stops spinning?

Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
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### Sum of angular momentum of all electrons in a magnet

Can the sum of angular momentum of all rotating electrons in all the aligned atoms in a permanent magnet have a significant contribution to the macro angular momentum of the magnet? If yes, why does ...
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### Modeling and Simulating Pendulum Motion

I've been having difficulty creating a mathematical model of a pendulum in my code. While there is plenty of info on general equations describing a the motion of a pendulum, I seem to be having ...
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### Intrinsic angular momentum in classical mechanics

Please note, I am only interested in classical mechanics discussion on this. Please do not involve quantum mechanics. Inspired by this question: Is Angular Momentum truly fundamental? My question ...
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### Dynamics of moment of inertia

I'd like to be able to determine the angular acceleration of a system of two rotating masses, which are connected so as to have a variable mechanical advantage between the two. My background with ...
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### How long for a frictionless top to fall over?

We've previously discussed why it is that spinning tops do not fall over, see: Why don't spinning tops fall over? However, as the highest rated answer notes, the angular momentum of the spinning top ...
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### Could life survive a pole shift caused by an asteroid collision?

Could life on earth survive a large pole shift caused by an asteroid collision? I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
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### Rotation angle of a giant lily when a child crawls on its rim

Below is a picture of Giant Water Lily. Scientific Name: Victoria Amazonica. Leaves of some of these could be as big as 3 m diameter and carry a weight of 45kg spread evenly and can support a child. ...
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### Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
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### Period of Precession [closed]

I'm trying to find the period of precession for a gyroscope. Now I was able to find the angular precession rate, which was 1.132 rad/s, but I have no idea how to convert this to a 'period', and google ...