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10
votes
3answers
485 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
130 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
376 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
166 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
83 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
89 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
575 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
136 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
295 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
1k 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
158 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
275 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
247 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
159 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
369 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
352 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 ...
16
votes
3answers
2k 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
306 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
161 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
213 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
209 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
206 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 = ...
3
votes
1answer
438 views

Intuitive explanation for why same force applied farther from a hinge causes larger angular acceleration than if applied closer?

A standard example of a problem involving torque is opening a door - the same force F applied far from the hinge causes a larger angular acceleration than if applied close to the hinge. I always had ...
7
votes
6answers
9k views

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 ...
3
votes
1answer
1k views

Elastic collision of rotating bodies

How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics? I'm writing simple physics engine, but now only simulating ...
2
votes
1answer
603 views

Deriving torque from Euler-Lagrange equation

How could you derive an equation for the torque on a rotating (but not translating) rigid body from the Euler-Lagrange equation? As far as I know from my first class in Classical Mechanics, there is ...
5
votes
7answers
1k views

What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?

Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating ...
4
votes
2answers
1k views

Which is the axis of rotation?

This should be simple, but it keeps bothering me. If a rigid body has no fixed axis, and a torque (defined relative to a point $A$) is applied, it will rotate around $A$. But often I can also ...
1
vote
2answers
536 views

Kinetic energy of a cylinder

It is a long cylinder (you can approx $R=0$), and it has a fixed point in one os its ending points, it's rotating on a plane and I have to calculate the kinetic energy from reference systems situated ...
2
votes
2answers
243 views

Force and Torque Question on an isolated system [duplicate]

If there's a rigid rod in space, and you give some external force perpendicular to the rod at one of the ends for a short time, what happens? Specifically: What dependence does the moment of inertia ...
4
votes
1answer
552 views

Can any physical rigid body be represented by an ellipsoid with the same angular dynamics?

According to wikipedia, the inertia tensor of an ellipsoid with semi-axes $a,b,c$ and mass $m$ is $\left[\begin{array}{ccc} \frac{m}{5}(b^2+c^2)&0&0\\ 0&\frac{m}{5}(a^2+c^2)&0\\ ...
2
votes
2answers
245 views

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 ...
2
votes
3answers
117 views

Reference for the predictability of rigid body dynamics

I'm looking for a reference, journal article, paper, etc. that supports the idea that classical mechanics, in particular rigid body dynamics, is largely predictable. A view coming from the background ...
8
votes
1answer
382 views

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 $ab$, ...
1
vote
1answer
114 views

Rigid body/moment of inertia problem

I have a homework assignment about rigid body dynamics. Take a disc of radius $r=2m$ with uniform mass density $\rho=1$ $kg/m^2$ in the x-y plane, resting in an inertial frame. At some instant, a ...
0
votes
2answers
426 views

Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
2
votes
2answers
2k views

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 ...
5
votes
3answers
812 views

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 ...
1
vote
4answers
736 views

Understanding Tensors

I don't seem to be able to visualize tensors. I am reading The Morgan Kauffman Game Physics Engine Development and he uses tensors to represent aerodynamics but he doesn't explain them so I am not ...
1
vote
2answers
175 views

Unexpected potential energy increase during Tic-Tac drop

I dropped a Tic-Tac: (no worries, it happened before), and I noticed as it bounced on the floor that it would first jump 20 cm high, and at the next bounce for instance 50 cm high. Shouldn't it ...
7
votes
3answers
96 views

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 ...
2
votes
1answer
263 views

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 ...
1
vote
3answers
3k views

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 ...
5
votes
6answers
1k views

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, ...
0
votes
1answer
623 views

How to calculate the coefficient of restitution for 2 bodies?

I have 2 rigid bodies (from different materials) in a collision. As you know I should have the coefficient of restitution value to get the velocities after collision. What is the information/values ...
2
votes
4answers
400 views

how to represent the effect of linking rigid-bodies together?

I have 2 rigid-bodies (b1,b2) if i linked one to the other (as if they are conjoined together) , how to represent b1 effect on b2 and b2 effect on b1 Is there any LAW that affect the ...
4
votes
1answer
646 views

How do you combine two rigid bodies into one?

With respect to some fixed frame of reference, given the inertial tensors, positions, orientations, and angular and linear velocities of two rigid bodies, how do you combine them to make a single ...
7
votes
2answers
910 views

How fast does force propagate through matter? [duplicate]

Possible Duplicate: Is it possible for information to be transmitted faster than light? Consider the following thought experiment. You have a long perfectly rigid beam (for the sake of ...
0
votes
1answer
630 views

Applying a force on a rigid body on a certain point

I have a rigid body with an origin point (at the center of mass). I want to apply a force on a certain point. So what is the force applied to the origin of this rigid body? Description image: ...
2
votes
0answers
156 views

What kind of shape has the lowest flutter wind speed?

What kind of shape has the lowest flutter wind speed and is the most unstable? I mean for rigid body. Thanks Yes, I know many factors affect the flutter in a MSD system (for rigid body), however ...