# Tagged Questions

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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### Why does this object periodically turn itself?

See below gif image taken from here. Or see this Youtube video about 30 sec in. Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? ...
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### Stability of rotation of a rectangular prism

I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions ...
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### Angular momentum with respect to the centre of mass

I have been told [Warning: I leave this because it's what I asked and allows to understand the dialogues in the comments, but Azad, whom I thank, has pointed that the formula does not hold in general ...
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### Degree of freedom paradox for a rigid body

Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$. As the distance between any two points in a rigid body is fixed, ...
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### Variable mass dynamics: Particle and Rigid Body

I'm encountering some issues in the understanding of some basic concepts about the dynamics of variable-mass particles and rigid bodies. For what I found, for example reading On the use and abuse of ...
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### 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 ...
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### What do people actually mean by “rolling without slipping”?

I have never understood what's the meaning of the sentence "rolling without slipping". Let me explain. I'll give an example. Yesterday my mechanics professor introduced some concepts of rotational ...
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### How can the contact point of rolling body have zero velocity?

They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion?
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### Defy gravity torques with gyroscopes?

Context On the following drawing, a platform is hung from the ceiling not exactly from its centre of gravity. Because of this it can't sustain an arbitrary orientation for long; I want to increase ...
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### degree of freedom of a rigid body 5 or 6?

I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only ...
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### Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
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### How do I handle elastic contacts in a simulation with friction [closed]

I'm trying to simulate a wheel as it hits the ground. Problem 1 Suppose a disc is dropped from a height. It has initial velocity of $-x,-y$ caused by throwing and gravity. It has no initial angular ...
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### Centre of instantaneous rotation problem

Is there a point of Centre of Instantaneous Rotation (CIR) for every type of motion or only for cases of rolling?
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### conceptual doubt in method to find moment of inertia about an axis

I asked this question before about whether I can take a component of angular velocity along another axis and say that the body spins about that axis with that component. Now I have another doubt: ...
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### 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 ...
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### How to combine these equations of constraint?

I want to model a nonholonomic system of an arbitrary rotating disk in 3D, which rolls without slipping, and doesn't have to stay vertical. (think spinning a penny on the table) I want to use the ...
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### Is there an equivalent of a scalar potential for torques?

For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from $$\mathbf{F} = -\nabla V$$ Suppose a rigid body is placed inside this ...
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### How to determine the probabilities for a cuboid die?

Imagine we take a cuboid with sides $a, b$ and $c$ and throw it like a usual die. Is there a way to determine the probabilities of the different outcomes $P_{ab}, P_{bc}$ and $P_{ac}$? With $ab$, ...
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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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### Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Rigid body dynamics of tossing of a coin

While tossing a coin, it is commonly experienced that you get a head, if you toss it up with the head side up, and a tails if you toss with the tails side up. Is there a mathematical proof of this ...
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### Rigid body rotation about fixed axis with angular velocity not constant in magnitude

I'm trying to understand the properties of angular momentum in the rotation of a rigid body around a fixed axis $z$, when the angular momentum $\vec{L}$ is not parallel to the angular velocity ...