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0
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2answers
57 views

Inertia matrix of a rod rotating about an axis [on hold]

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
25 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, ...
0
votes
1answer
30 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
49 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). ...
0
votes
0answers
12 views

Can we always apply a pure torque at arbitrary positions on an object in practice?

I want to apply a pure torque to an object, say a square box on the ground. And I also require that the torque is generated on the corner of the square, not the center of mass. Is there any way for me ...
1
vote
1answer
35 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
votes
0answers
52 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 ...
0
votes
0answers
23 views

An easy source to understand classical dynamics — Rigid body Rotation [duplicate]

I've been having an extremely hard time at understanding rigid body rotation. The source that I'm currently studying from has been suggested by 't Hooft on his webpage. It's by Richard Fitzpatrick. ...
1
vote
2answers
47 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 ...
0
votes
1answer
80 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
54 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
43 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
vote
0answers
36 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
50 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). ...
2
votes
0answers
66 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
24 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
vote
1answer
42 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 ...
0
votes
0answers
28 views

Quantify the “stiffness” of a 3 axes gyroscope

Imagine a platform on a spherical joint/guimbal at its centre. The platform has 3 reaction wheels that act as a 3 axes gyroscope by rotating at a middle setpoint. The system {platform;wheels} has its ...
2
votes
2answers
148 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
0answers
70 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
votes
1answer
70 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
54 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
62 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
108 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
vote
2answers
105 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
51 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
112 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
168 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 ...
1
vote
3answers
178 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 $v_0$ ...
0
votes
1answer
110 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
172 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
158 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
76 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
85 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
542 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
106 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
265 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
883 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
140 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
254 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
184 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
152 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
286 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: ...
21
votes
2answers
316 views

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 ...
11
votes
2answers
1k views

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 ...
0
votes
1answer
260 views

Confusion in connected pulleys problem

I'm having some troubles in understanding why my reasoning doesn't work in the following problem: Problem Two pulleys of mass $m_1$,$m_2$ and radius $r_1,r_2$ are connected by a belt (like chain ...
0
votes
1answer
132 views

Can a pushed plank beat light and break the laws of physics? [duplicate]

Imagine you are one lightyear away from a photon sensitive (light sensitive) switch. So it is obvious that light would take one year to reach to the switch. Now I have a one lightyear long plank. I ...
3
votes
2answers
175 views

Extension to continuous in proofs of rigid body mechanics

I'm studying rigid body mechanics and I've seen several proofs of properties related to total angular momentum, kinetic energy, etc. that all regard discrete set of points. For example, to show that ...
2
votes
1answer
197 views

A different proof for 6 degrees of freedom

I want a different proof of 6 degrees of freedom of a solid object made of $\ N$ particles. I am thinking along these lines: Definition of rigid body is $\ modulus[\vec{r_i}-\vec{r_j}]=constant \ ...
2
votes
2answers
176 views

Deriving $T = F\ r = I\alpha$ for a rigid body

For a single point mass : $\tau=F_{t}r=ma_tr=(m r^2)\alpha = I\alpha$ For multiple point masses bound together : $\sum \tau_i = (m_ir_i^2)\alpha = I\alpha$ But how do we go from that to $I\alpha = ...