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2
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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 ...
2
votes
1answer
238 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
290 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 = ...
2
votes
1answer
918 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 ...
2
votes
2answers
99 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
votes
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
2answers
269 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 ...
2
votes
1answer
330 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 ...
2
votes
3answers
128 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 ...
1
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4answers
880 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
69 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
vote
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 ...
1
vote
2answers
36 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 ...
1
vote
1answer
176 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 ...
1
vote
2answers
140 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. ...
1
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4answers
179 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
1answer
144 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 ...
1
vote
2answers
204 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 ...
1
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3answers
4k 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 ...
1
vote
1answer
54 views

Approximating the moment of inertia of a quadcopter [on hold]

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 ...
1
vote
1answer
53 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 ...
1
vote
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 ...
1
vote
1answer
423 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 ...
1
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2answers
106 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
1answer
92 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
1answer
208 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
2answers
743 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 ...
1
vote
2answers
680 views

How are Euler's laws of motion applied to gyroscopes?

Euler's laws of motion for a distributed mass are: $$F = \frac{d}{dt} MV_{cm},\ N = \frac{d}{dt} L$$ $F$ are the sum of the external forces, $M$ the total mass, $V_{cm}$ the velocity of the centre ...
1
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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 ...
1
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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 ...
1
vote
2answers
96 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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0answers
40 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 ? ...
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?
1
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0answers
208 views

point-particle vs rigid-body [closed]

As pointed out here point-particle-based modeling can lead to very inaccurate predictions. Could you give an example where point-particle-based model describes reality accurately enough and one where ...
1
vote
0answers
56 views

Terrestrial Space Elevator Construction - Plausability

Framework If there was a cable constructed at the equator about the circumference of the Earth, and if this cable had sufficient strength to remain intact while erect, call this tensile strength T. ...
1
vote
1answer
68 views

Collision Resolution System Adding Velocity Into System

In my 2-dimensional physics simulation, I have a rectangular rigid body 'a' with infinite mass (the floor), and a rectangular rigid body 'b' with finite mass above it turned at a slight angle. When ...
1
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0answers
35 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
vote
1answer
180 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 ...
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0answers
72 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 ...
1
vote
1answer
47 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 ...
1
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0answers
43 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 ...
1
vote
1answer
139 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 ...
1
vote
2answers
150 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 ...
1
vote
1answer
254 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, ...
0
votes
1answer
89 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
1k views

Tennis serving machine— How does a spinning ball bounce?

I have an idea of making a tennis serving machine. I will briefly describe what it is: The machine is configured to serve the ball at a fixed speed to the center of the left (or right) service court ...
0
votes
2answers
220 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
2answers
744 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
2answers
115 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). ...
0
votes
2answers
542 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 ...