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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0
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3answers
450 views

Proof that a force applied to the center of mass is the same as force applied off-center

There is a similar question that gives a bit of an explanation, but little mathematical proof here: force applied not on the center of mass I would like mathematical proof that shows that the ...
8
votes
1answer
679 views

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 ...
3
votes
4answers
366 views

Solving for motion of rotating rod using only Newton's laws?

I have a question that's been bothering me for years. Given a rod of uniform mass distribution with total mass $M$ and length $L$ that lies on a horizontal table (with one end fixed to the table ...
0
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1answer
185 views

Question about the parallel axis theorem

I've a question about the parallel axis theorem. So I'm perfectly OK with the derivation of the proof in 2D. However in the typical derivation they just say this in my textbook "Because the Zi ...
1
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0answers
36 views

Is having full information about the resonances of a rigid body equivalent to having full information about its material parameters?

Lets say I have a mechanical system whose mechanical resonances (mode shape and frequency) I can measure with perfect accuracy. Is this theoretically equivalent to knowing the materials parameters, ...
1
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1answer
213 views

Solid-body rotation of fluid in polar coordinates: How to compute the stress tensor

In a course on continuum mechanics, we are given an exercise concerning solid-body rotation of a fluid in polar coordinates. In the first parts (feel free to correct any errors here) we are tasked ...
1
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0answers
77 views

A rigid rotating rod that breaks in two pieces

Suppose we have a rigid rod of lenght $L$ and homegenous mass density. One of its extreme points, say $P$, is fixed so that the rod can rotate around the axis passing in it. Initially the rod is held ...
0
votes
1answer
122 views

Balancing stick on hand - inverted pendulum motion

How do I calculate the velocity and acceleration of a stick that is vertically on my hand? How fast and far do I need to move my hand from side to side to keep balancing the stick? Assuming that we ...
3
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2answers
409 views

Consider a horizontal surface with or without friction. Ideally, will a wheel rolling without slipping roll forever in both cases?

Suppose a wheel is rolling smoothly on a horizontal plane i.e., it is rolling without slipping. Now let's take the two cases of the horizontal plane: It has friction It is frictionless In the ...
0
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2answers
258 views

Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
0
votes
1answer
111 views

Coordinate System vs. Angular Properties vs. Centroid

Please help me check my understanding related to the rotational motion of a 3D rigid body after reading some Physics textbooks and googling for some more materials (e.g., Wikipedia's Torque, ...
1
vote
1answer
458 views

Torque and angular acceleration with bicycle wheel

This might be a simple problem for many of you. However, please help me understand it too. I have been looking trough a lot of materials online, and I still have the following questions, that would ...
2
votes
3answers
687 views

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). ...
1
vote
1answer
48 views

Is there no problem in thinking of any motion of a rigid body as a composition of translational motion and rotation w.r.t center of mass?

Sometimes when I work on mechanics problems, I wonder if this analysis is always valid. Couldn't there be some motion of a rigid body that cannot be expressed as a composition of translational ...
0
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0answers
291 views

Calculating Inertia Tensor with Parallel Axis Theorem

Say you have a solid you are approximating as n point masses at different points in a 3D space. Each point mass has a mass of 1. The origin is not the center of mass. All the points have location ...
1
vote
2answers
108 views

Eulerian Angles — Why three rotations can transform fixed frame into body frame?

"In general, if we restrict ourselves to rotations about one of the Cartesian axes, three successive rotations are required to transform the fixed frame into the body frame" The origin of our fixed ...
1
vote
2answers
857 views

Derivation of Euler's equations for rigid body rotation

Sorry for using this image, but I thought this was the most convenient way of asking this question. Please zoom in. I do not understand from the line, "Now, in the body frame $T = (T_{x'}, T_{y'}, ...
0
votes
1answer
94 views

When does the angular momentum point in a different direction from the angular velocity?

I read this somewhere: $$\mathbf{L} = \tilde{\mathbf{I}}\mathbf{\omega}$$ In general, the angular momentum vector, $\mathbf{L}$, obtained from Equation above, points in a different direction to the ...
0
votes
1answer
53 views

Force on a line

Say you have a rigid line of mass $m$ and length $\ell$ along the $x$ axis and you apply a constant force $f$ at one end in a direction that is always perpendicular to the line, starting in the $y$ ...
1
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0answers
44 views

Loaded die problem

A loaded die has an uneven mass density distribution. A given die is constructed from a square pyramid of material with mass density $\rho_1$ whose bsase lays on the face marked "1",with the rest of ...
0
votes
2answers
120 views

Rigid body rolling quesion

Hey, im having a bit of trouble with the problem in the added photo. So, there is the cylinder which is attached by a massless rope to a massless pulley, to a box (assume it is a pointed object). ...
4
votes
1answer
212 views

Understanding gyroscopes

Considering the typical situation of a rotating bicycle wheel held by one end of its axle by a rope tied to the ceiling: gravity torque is the time derivative of the angular momentum, and in this case ...
0
votes
1answer
61 views

Rotatory motion of uniform disk

Consider a uniform disk rolling without slipping with a certain constant angular velocity.Firstly it is moving in sufficiently rough surface.What will happen if it crosses the rough surface and just ...
1
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1answer
146 views

Center of rotation and trajectory of a rigid body in a plane with applied *fixed* forces

This is my first question so please excuse me if my format is a bit off. Given a 2D rigid body with forces applied to it in such a way that the angle the force vector makes with the surface of the ...
2
votes
2answers
429 views

Rod Falling on Frictionless Surface

A rigid rod with mass m is initially held at an angle with respect to a frictionless plane by a string. Then the string is cut. What happens to the rod? My intuition suggests that the rod should slide ...
2
votes
1answer
266 views

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 ...
0
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1answer
257 views

Rigid body problem in 2d

I have some questions about this exercise: In an horizontal plane, a $OA$ bar with mass $m$ and length $a$ moves, with another bar $AB$ (same mass, double length) attached in the point A. In the ...
0
votes
1answer
179 views

Rigid body problem

I have some doubts about the next excercise: A bar of length $2a$ and mass $m$ moves freely with both of its extremes on a ring of radius $\sqrt2a$. The ring can rotate freely in a certain ...
1
vote
1answer
93 views

Motion of rigid body system in absense of work

In the absence of work on the system, is there a closed form equation for the motion of a set of constrained rigid bodies (let's say, using Revolute (ie: simple pivot) constraints)? If the bodies are ...
1
vote
4answers
197 views

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?
1
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2answers
152 views

Rigid bodies - the wheel

As I've been taught lately in my mechanics course: the wheel has a unique property: at every moment of motion, the touching point between the wheel and the ground is not in movement and ...
0
votes
1answer
69 views

How does this formula for calculating the “mass sum” in a collision translate to 3D?

According this tutorial, formula number 5: $$j = \frac{-(1 + e)((V^{A} - V^{B}) * t)}{\frac{1}{mass^{A}} + \frac{1}{mass^{B}}}$$ translates into formula number 6: $$j = \frac{-(1 + e)((V^{A} - ...
2
votes
2answers
267 views

Angular Momentum of a rigid, extended object

Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum. It is often said that an object that has been thrown up in the air ...
1
vote
1answer
212 views

Newton's second law for rotation

Can the second law of motion for rotation, $\vec{\tau}=I \vec{\alpha}$, be used for any axis? Is there any case that acceleration $\vec{\alpha}$ is not in the direction of applied torque ...
2
votes
3answers
410 views

Ideally speaking, will a rolling disk with no slipping come to a stop because of friction from the ground?

Consider a rotating disk on a horizontal plane with static friction. The contact point of the disk with the plane has null instantaneous velocity. Assuming the center of the disk has fixed $v_0$ ...
13
votes
3answers
1k views

What is the physics of a spinning coin?

When we spin a coin on a table, we observe 2 things: It slows down and stops after sometime. It does not stay at just one point on the table but its point of contact with table changes with time. ...
0
votes
1answer
176 views

2D. Force applied at angle to body, where translational vector will be directed?

I'm not a physicist and just making some research by the way of creating simple physics simulator, because of that, sorry if this is very dumb question, but I really need help with it. Let's assume ...
3
votes
1answer
680 views

What is a bilateral constraint?

In the realm of mechanics/rigid body dynamics, can anyone tell me what a bilateral constraint is? Can't seem to find any information on the exact definition, just uses of it such as "considering only ...
0
votes
1answer
182 views

Net torque on an object

Suppose that a cord is wrapped around the rim a disk of radius $R$. The disk is allowed to rotate around its central axis (the line passing through the center and perpendicular to the disk surface). ...
0
votes
0answers
90 views

How can I simulate a rigid bounced from a wall?

How can I simulate a rigid sword bounced from a wall and hit the ground(like in physical world)? I want to simulate a simple animation. The sword is controlled by a center/mass point.(Actually ...
-1
votes
1answer
113 views

Normal force at the bottom [closed]

A solid sphere of mass $m$ is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the the hemisphere is kept horizontal, find the normal force ...
2
votes
1answer
772 views

How come a rigid body has 6 degrees of freedoms (DOFs) ? Isn't velocity a DOF?

For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?
0
votes
0answers
199 views

Torque of Air Resistance on Ellipsoid

Imagine an non-rotating arbitrary free, rigid ellipsoid with in some arbitrary direction with velocity $\vec v$. Assume linear drag ($\vec F=KA\vec v$ for some constant K, where A is the cross section ...
3
votes
1answer
415 views

Euler's equations of rigid body motion from least action principle

I would like to derive Euler's equations of rigid body motion from least action principle. Suppose we are in free space so we have no gravity so Lagrangian is equal to kinetic energy. $$ L = T = ...
2
votes
2answers
2k views

Angular Velocity expressed via Euler Angles

On the top of the fourth page from here, the author trivially derives the components of angular velocity, expressed via Euler angles of the system. I fail to understand how the components of angular ...
1
vote
1answer
264 views

Torque on a Box

I think I'm missing something with torques. I seem to have gotten myself confused. I have a box that's centered at ( 0 , 0 , 0 ) with length ( $x$ dimension ) = 1 , width ( $y$ dimension ) = 0.25, ...
-1
votes
1answer
332 views

A Rolling Quarter [closed]

A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius $R=4 \text{cm}$. The plane of the coin is tilted at an angle of $\theta=45^{∘}$ with ...
2
votes
2answers
372 views

Is it better to build a space elevator from GEO down to the surface of the Earth?

Having just finished Arthur C. Clarke's "The Fountains of Paradise", Clarke seems to make a distinction between starting construction of a space elevator from geosynchronous orbit and working on our ...
6
votes
2answers
201 views

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 ...
2
votes
2answers
502 views

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: ...