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2answers
93 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...
1
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1answer
37 views

Approximating the moment of inertia of a quadcopter

I want to compute an approximated moment of inertia for my quadcopter: my idea is to take the frame and the electronics, approximate it as a sphere in the center of mass $M$ and radius $R$ (with ...
0
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0answers
19 views

Precession problem with a rotating cross [on hold]

I'm attempting a homework question about advanced classical physics. This problem describes a light rod between two poles with a cross at the middle rotating, what happens if we remove one of the ...
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12answers
3k views

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?
3
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1answer
95 views

Tensor components change under rotation-translation

I am currently working on a research project in a non-physics field, where I would like to work on a very constrained 2nd order tensor (3x3, symmetric, traceless). The tensor represents probability of ...
2
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2answers
96 views

Torque on puck moving on plane without friction

We have two pucks moving on a plane without friction. On one of them a force is applied on it's center of mass. On the second a force of equal magnitude is acting tangential to the puck and at a ...
2
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1answer
115 views

Equation of motion for the center of mass of a rigid body

The center of mass of a rigid body is given by: $$ \vec{r}_c = \frac{1}{M} \sum_i m_i \cdot \vec{r}_i $$ with $M = \sum_i m_i$ the total mass or $$ \vec{r}_c = \frac{1}{M} \int \vec{r}\ ' \cdot ...
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0answers
46 views

Contact between two rigid bodies. How does contact force is distributed in the contact surface?

We have a rigid body with some scalar function of vector argument, which describe density of body at concrete point in space. The body lie on the table in the stable state, elements of it doesn't ...
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1answer
237 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 ...
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0answers
19 views

Calculate angular velocities and alpha values?

A lightweight bar, stiff stick of length L, at either end are two small spheres of mass $m_{1} = m_{2} = m$. Bar may turn in vertical horizontal axis passing through point O on the way its a bar ...
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1answer
55 views

Representation Of Linear Velocity as Cross Product

Why is linear velocity represented as cross product of angular velocity of the particle and its position vector? Why not vice versa? (Consider rigid body rotation)
1
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1answer
51 views

Does precession of a rigid body change instantaneously?

I read some explanations of precession; this side for example summarizes briefly almost all what I have understood so far. But one thing bothers me: Following all this formulas, the precession ...
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10answers
16k 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 ...
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4answers
5k 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
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0answers
26 views

Rotation of Thin street sign

I am attempting to complete a home question in which a shop sign in the shape of a thin rectangle of size p x q (with q being the longer side), and mass m, that rotates about an axis that passes ...
0
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0answers
31 views

When a force applies to a rigid body at point, then does every part of the body experience the same kind of force?

Suppose that a rigid body is static under the action of several forces that are applied at different part of the body. Then is it true that if one divides the body into small pieces, then each piece ...
2
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1answer
45 views

Ball's opposite rotation caused by friction

Assume that you push a ball like in the picture (along the red line) with your hand with a some force. The ball will move forward while its rotating in this way: And after some movement, the ball ...
13
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3answers
929 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. ...
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1answer
24 views

Pure Rolling from a stationary surface onto a moving surface

Suppose a sphere rolls without slipping on horizontal stationary ground. Now, suppose the sphere rolls onto a surface which is moving at some velocity with respect to the previous stationary ground. ...
3
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3answers
103 views

Uniqueness of the angular velocity

Let us consider the most general motion of a rigid body. Two arbitrary points of the body, $i$ and $j$ must not change their distance $d_{ij}$ during motion. Therefore,$$(\vec{r}_j - \vec{r}_i)^2 = ...
2
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1answer
68 views

components of angular velocity?

Let $\vec \omega = (\omega_1, \omega_2, \omega_3)$ be the angular velocity of a rigid body with respect to the body frame, where the body frame is right-handed orthonormal. I have gathered 2 ...
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3answers
394 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 ...
3
votes
1answer
45 views

In a rigid rotor, are there “elegant” orientation coordinates that are conjugate to angular momenta?

I just was looking at the big bag-of-math wikipedia article on rigid rotors, and the section on the Hamiltonian form bugs me a bit since they are using Euler angles to represent the orientation. As a ...
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2answers
68 views

What will happen if I remove a nail which stops a plank from moving on a smooth floor because of a solid sphere pure rolling on it?

What will happen if I remove a nail which stops a plank from moving on a smooth floor because of a solid sphere pure rolling on it?The plank has it's upper surface which is in contact with the sphere ...
1
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1answer
38 views

Running Euler's disk in a superfluid

I was considering the toy Euler's Disk, a video can be found here: http://www.youtube.com/watch?v=mVl2CBG_h2s I was interested in understanding the behavior of the disk particularly in vacuum and in ...
2
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2answers
128 views

Determine reaction forces on square frame

The square frame consists of four identical homogeneous rods of mass $m$. It lies in the vertical plane and can move in it due to the wheels situated in A and B. These wheels can slide ...
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2answers
35 views

Does a bungee cord have a moment of inertia?

Does a bungee cord have a moment of inertia? I'm trying to understand to what extent a body must be rigid in order for the moment of inertia to be defined for that body. Since the distance between ...
0
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1answer
55 views

Why falling camera/objects rotate and then stabilize?

I was going to ask something very similar to this question (which hasn't been answered). Basically a camera fell from an airplane and it began to rotate (maybe because initially it was put in rotation ...
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0answers
22 views

How to prove the relation between the rate of change of a vector in space coordinate and in body coordinate?

I'm learning Goldstein's classical mechanics, and in chapter 4.9 he prove such an operator equation $(\frac{d}{dt})_s=(\frac{d}{dt})_r+\omega \times$ In the proof, he takes the space and body axes as ...
0
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0answers
29 views

Force and Torque being applied off-center due to magnetic forces [duplicate]

Say that I have two magnetic dipoles, one of which is rigidly attached to a freely movable inflexible body at some point that is not at the body's center of mass, while the other is fixed in space. ...
1
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1answer
46 views

Degrees of Freedom for an Asymmetric top

How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then?
0
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0answers
121 views

Combining Moment of Inertia Tensors

In a physics simulation of rigid bodies, if I have a cube with a known mass and moment of inertia tensor, and I attach it to another cube with a known mass and moment of inertia tensor such that its ...
3
votes
2answers
189 views

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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1answer
104 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
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1answer
115 views

How do two rigid bodies with different 3rd moment of inertia rotate differently?

If rigid bodies $R_1$ and $R_2$ has exactly same total mass $M$, central of mass, and rotational inertia $I$, but different third moment of inertia $M_3$, how would they move/rotate differently? ...
3
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3answers
250 views

what make the bottom portion of a wheel in rolling motion move?

As I just learn about the rolling motion which is the combination of pure translation and pure rotation. The top portion of the rolling body has the speed of double speed at the center of the object ...
4
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1answer
204 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 ...
3
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0answers
152 views

How do I treat the Lagrangian in the case of a rigid body?

Here's Exercise 1.11 from Goldstein's Classical Mechanics 3rd edition (the first one after having derived the Lagrangian basically): Exercise 1.11: Consider a uniform thin disk that rolls without ...
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0answers
39 views

Rigid body translation and the moment about a point

ok the statement of the moments , beside the fourth car image How there is a moment about the point A although there is only translational motion , is not the car only moving and not rotating ? ...
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0answers
14 views

Robot speeds in body frame

I am building a robot with two wheels (and differential drive) and I am trying to make it have the same performances over very different loads (an order of magnitude between the ), so I decided to try ...
5
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6answers
2k 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, ...
1
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4answers
879 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
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1answer
171 views

Feynman's explanation of parallel axis theorem

In the book Feynman's Lectures on physics volume 1 chapter 19, He explains prallel axis theorem as follows. Suppose we have an object, and we want to find its moment of inertia around some ...
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1answer
50 views

Calculating the components of angular momentum of a rigid body

You have a rigid body with 1 fixed point in space (the origin). It's self-explanatory how to get the following equation for the angular momentum: $\vec L = \sum_n m_n\vec r_n\times\vec v_n$ ...
5
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3answers
988 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 ...
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0answers
40 views

Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
2
votes
1answer
119 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
2
votes
1answer
252 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
174 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 ...
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2answers
132 views

Applying a force on a rigid body which is used to create torque

In the above picture, I have a rigid body, in turquoise, which is connected to a point, the red circle. The dotted lines are used to divide objects or lengths, they are not part of the rigid body. ...