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Questions tagged [rigid-body-dynamics]

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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Aspect angle of object [on hold]

How can I find aspect angles with respect to ground of an object in at height $h$. Object is rigid body with pitch angle $\theta$ in body coordinate.
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28 views

Im getting answer as t=5wR/8ug and w.f. =w/4 but its not in the options please help [on hold]

31* A solid disc of mass m and radius R is spun with an angular velocity w about its axis and then set into motion on a rough horizontal plane with a horizontal velocity v = Rw/4 while keeping the ...
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0answers
13 views

Torque, Rotational motion [duplicate]

Slow precession can be used to determine a much more rapid rotational frequency. Consider a top made by inserting a small pin radially into a ball (a uniform sphere) of radius R = 6.0 cm. The pin ...
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1answer
8 views

Rolling without slipping around a fixed axis (practice exam) [closed]

Everything is pretty much given in the image. We had to find the relation between omega-p and omega-s The answer is omega-p * (r+a*cos(alpha)) = omega-s * a It says that the in the inertial frame ...
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2answers
71 views

Mechanics: angular momentum of disk

I am studying mechanical engineering and I've got a problem with the angular momentum of objects that have a rotation which is rather complex to describe like the following: The shaft rotates around ...
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1answer
45 views

Torques in Euler equation

The Euler equation is given by $$\mathbf I\dot{\boldsymbol \omega}+\boldsymbol\omega\times \mathbf I\boldsymbol\omega= \mathbf M.$$ Also see here. It explains that The expressions for the torque in ...
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1answer
18 views

Lagrangian of a Heavy Symmetrical Top - Inertial or Non-inertial Frame?

I'm having some confusion with the analysis of a symmetrical top (specifically, a heavy top, but this is not very important for the question). Following Landau and Lifshitz's Mechanics, on page 110 ...
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1answer
31 views

Kinetic energy of a gyroscpoe toy

Why the energy only has rotational part $\frac{1}{2}I_1\omega_1^2+\frac{1}{2}I_2\omega_2^2+\frac{1}{2}I_3\omega_3^2$? The center of mass also moves in general.
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Angular velocity of a spinning top

I have several questions about spinning tops/rotating rigid bodies. What is the $\omega$? Is it the angular velocity observed outside or with the body? Personally, I do not think one can measure it ...
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1answer
29 views

Deriving velocity in rolling without slipping in another approach

I want to derive the velocity of a point P on a surface of a cylinder rolling on a flat plane, by considering the rolling as instantaneous rotation with repect to the contact edge line E of the ...
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1answer
39 views

What happens when you try to turn a gyroscope with high torque?

I apologize for my lack of basic understanding of gyro-physics, I tried looking up internet, but couldn't find any answer for this particular question. I have been told that if I apply torque to the ...
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2answers
38 views

About which axis equation of torque must be written? [closed]

Precisely define axis of rotation. Should the axis of rotation be always fixed? Why? In a rotating rigid body torque can be anything about different axis. So about which axis we should write the ...
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0answers
66 views

Why does conservation of energy appear to be violated? [closed]

I am currently working on a rigid body simulator. Before getting proper collision and rotations working, I decided to simulate the collision of spheres as axis-aligned objects. The simulation works ...
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0answers
26 views

Slipping of a rod -dynamics

A uniform rod of mass m is placed at right angles to a smooth plane of inclination $\alpha$ with one end in contact with it. The rod is then released. Find reaction of the plane when the ...
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0answers
31 views

Basic doubts about dynamics of a rod [closed]

I have few doubts in the given solution. It says there is no force along the plane but $mgcos\alpha$ is acting along the plane ? As given, $A$ is used as orgin. Then how come x-co-ordinate of $G$ is ...
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1answer
71 views

Using Euler equations to solve for torque

I am trying to solve the torque needed to rotate a rectangular plate of sides $a$ and $b$, about a diagonal with constant angular velocity $\omega$. Euler equations are given by, $$ I_1\dot{\omega}...
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3answers
71 views

How many moment of inertia about center of mass exist?

So imagine we have a rigid body and we want to find the moment of inertia about center of mass . Doesnt exist infinite axis that pass trough center of mass therefore infinte moment of inertia? Do they ...
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0answers
97 views

Deriving moment of inertia of a solid sphere [closed]

I have been trying to calculate it on my own, but the answer I get is different to the one I can find everywhere else, so I have to be wrong. My attempt was a very straightforward one. I used ...
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2answers
106 views

How to choose the perpendicular axis?

This site https://en.wikipedia.org/wiki/Perpendicular_axis_theorem says: Define perpendicular axes $x$, $y$, and $z$ (which meet at origin $O$) so that the body lies in the $xy$-plane, and the $z$-...
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1answer
75 views

Integrating rigid body equations for a game engine simulation

I'm a mechanical engineer who's trying to implement a physics engine for a 3D game simulation, so I apologize for being incorrect or simply ignorant of some aspects of computation. I'm implementing ...
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1answer
44 views

Relation between rotation vector derivative and angular velocity when the rotation angle is constant

$\def\va{\vec{\alpha}} \def\vw{\vec{\omega}} \def\vn{\vec{n}}$Let $\va(t)$ be a rotation vector such that its direction is the rotational axis and its length $\alpha=|\va|$ is the angle describing the ...
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1answer
42 views

Angular acceleration in rigid body dynamics

I'm a little confused. In rigid body dynamics, could we write $\alpha = \frac{a}{r}$ everywhere in combined translational and rotational motion? If not, then where we could write it?
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2answers
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How does the COM of a rigid body always move as if only external forces influence it?

There's this example in my physics textbook: It seems to suggest that the resultant of all external forces acting on a body tells you how the COM of the body is going to move. Now, I understand the ...
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1answer
103 views

Is torque always equal to the derivative of potential energy with respect to rotation angle?

For any three-dimensional rigid body, the applied torque on that body is defined as: $\vec{\tau} = \vec{r} \times \vec{F}$ where $\vec{F}$ is the applied force on the object (i.e. $-\vec{\nabla} U$) ...
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3answers
95 views

Is it possible to understand the Gyroscope Effect Intuitively?

A stationary wheel, with its axis tied only at one end, falls down, but a rotating wheel, with its axis tied only at one end, doesn't fall down. The explanation given everywhere is by the ...
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1answer
126 views

The Euler-Lagrange equations for rigid body rotation

The equations of motion for rigid body rotation are: $I\,\dot{\vec{\omega}}+\vec{\omega}\times I\,\vec{\omega}=\vec{\tau}$ How i can calculate this equations using Lagrangian method ? If i use $...
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0answers
76 views

Coin spinning on smooth table [closed]

A coin radius $r$ spins on a smooth table with its plane at a small angle $\theta$ to the horizontal. Show that the head on the coin, viewed from above, appears to rotate with angular velocity $\sqrt{(...
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1answer
37 views

In which scenarios is the derivative of mass moment of inertia ignored and taken into consideration for rigid bodies?

When taking the time derivative of Angular Momentum The first two terms represent the relative rate of change with respect to the coordinate system used. Most sources I have been reading state that ...
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2answers
161 views

What is the difference between precession and spin angles?

I was recently introduced to Euler Angles in a Dynamics course, but I am confused on the difference between precession and spin angles. Both precession and spin consist in rotating a coordinate system ...
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2answers
184 views

Degree of freedom in Lagrange's formalism

Degrees of freedom $=3K-N$ where $K$ is number of particles and $N$ is number of constraints. How to find the number of degrees of freedom for a rigid body which has both translation and rotation, ...
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1answer
36 views

Equivalent inertia at spherical joint in multibody tree

Consider a tree system of rigid bodies and spherical joints. Starting at an outermost body, I'd like to calculate its equivalent mass (which I'm guessing would be an inertial tensor or something) at ...
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2answers
60 views

Why does the sphere not roll?

It says in the first case that the sphere never rolls. Is it possible for a sphere to not roll and just slide?
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1answer
47 views

When and why are we allowed to treat a rigid body as a point mass?

When the subject Mechanics first taught, it is common that we explicitly state that the Newton's laws are valid only for point masses, and then we give examples of rigid bodies colliding with each ...
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1answer
148 views

Start of gyroscopic precession

Let's consider the classical example, the wheel hung by one side of the axle: ¹ When the wheel is not spinning, it will tilt down the free end of the axle first. When the wheel is spinning, it will ...
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0answers
96 views

Proof of holonomic constraints for a wheel on a track

I'm faceing a problem of a thin wheel of radius R rolling without slipping on a track (y = f(x); on xy-plan). The wheel plane stays vertical and tangent to the track at the contact point P. $\alpha$ ...
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1answer
185 views

Gyroscopic precession - Angular momentum in vertical direction

In the classic example of gyroscopic precession, the wheel starts to process, and now acquires a angular moment also in the vertical direction. Initial angular momentum was in a single plane. The one ...
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2answers
176 views

Is kinematics required to solve for the quaternion dynamics of a tumbling body?

I'm trying to solve for the rotational motion of a rigid body in the absence of external torques using quaternions in MATLAB. Assuming the axis of rotation as the unit vector $\begin{bmatrix}a_x & ...
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0answers
43 views

Matrix Euler’s rigid-body equation

Define the action $$S[g]=\displaystyle\frac{1}{2}\int^1_0 Tr(I(g^{-1}\dot g)~g^{-1}\dot g)~dt.$$ $I:SO(N)\to SO(N)$ denotes the endomorphism $\omega \to I(\omega)$ with $I(\omega)_{ij}=\omega_{ij}/...
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1answer
40 views

Uniqueness of Mass Moment of Inertia tensor

I was curious to know if there can exist two different objects (shape and/or mass distribution) that can have the same inertia tensor.
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2answers
266 views

The angular velocity

Is the angular velocity of a rigid body about any point the same as that about the axis of rotation. Also, can we even define angular terms (Angular Velocity, Angular Acceleration, etc) about any axis,...
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1answer
753 views

Relation between acrobat and principle of conservation of angular momentum

How the principle of conservation of angular momentum is used by an acrobat to rotate a few revolution while leaping throung the air?
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0answers
31 views

Velocity of the reverse/double domino effect

I've seen a lot of talking about the propagation velocity of the domino effect, and I've even read a very interesting paper called 'The Domino Effect' by Leeuwen which really satisfied me. And yet, I'...
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0answers
21 views

Can an ideal wheel roll indefinitely with friction? [duplicate]

When the wheel is in pure roll the work done by the static friction is zero. Does that mean the wheel can go on forever?
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3answers
666 views

How rotating body have same angular velocity and acceleration

Does a body rotating about a fixed axis have to be perfectly rigid for all points on the body to have the same angular velocity and the same angular acceleration
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0answers
55 views

Conservation of momentum $\vec{L}$ and $\tau$ equations

Is it possible to conserve angular and linear momentum of a rigid body from any frame or just from the ground frame of reference? My book says for reference point $A$ and $\omega$ of body about CM, $$...
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2answers
585 views

Why perpendicular axis theorem is applicable only for laminar (2-D)objects?

I was taught that perpendicular axis theorem is valid only for laminar objects and not for 3-D objects.I have difficulty in understanding this intuitively. I mean why would such a condition even ...
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2answers
207 views

Is it always true that a solid object(geometrical figure) has less moment of inertia than its corresponding hollow one? [duplicate]

what I mean is that,if you have two objects(one hollow and other solid): Lets say, a solid sphere and a hollow sphere and if you calculate moment of inertia of the two of them, you would find that ...
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0answers
156 views

Calculation of number of degrees of freedom of a rigid body

I was reading a paper called Exact calculation of the number of degrees of freedom of a rigid body constituted by n particles where a method is suggested on how to calculate the degrees of freedom of ...
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2answers
130 views

Torque Equation for a point other than the axis of rotation [duplicate]

I am having a problem while dealing with the so called torque equation τ=Iα, which I am describing with the help of an illustration. Please help me out. Consider a rod of length L and mass ‘m’ lying ...
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2answers
66 views

Explain the relative motion between two particles of a rotating rigid body

A rigid body is defined as a collection of particles in which distance between each pair of particles remains constant. I was taught that the motion of any one particle of the rigid body with respect ...