# 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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### Why Polhode is a circle in a symmetric body

Goldstein In the special case of a symmetrical body, the inertia ellipsoid is an ellipsoid of revolution, so that the polhode on the ellipsoid is clearly a circle about the symmetry axis. The ...
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### Does the height a person jumps from onto a rod, affect the rotational height of a rod?

I was explained in a lecture that if lets say, I jumped from height h and grabbed onto a vine, I would reach y height at the tip of the swing. But if I were to jump from 2h, I would still reach the ...
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### Why is stable rotation achieved about the long axis of a skateboard? [duplicate]

I've been preparing a video for my mechanics assignment and I've hit a deadlock. Basically, I want to prove that the long axis of a skateboard takes the least force to move around it.I figured that a ...
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### How one derives this formula? [closed]

Recently I have seen the following formula for motion of rigid body with a fixed point: $$\dfrac{dT}{dt}=\int\limits_{0}^{t}M_{O}(\tau)d\tau$$ and I have no clue how this formula is derived. Could you ...
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### Which way do Feynman's plates precess?

I assume people are familiar with the story of Feynman watching students toss dinner plates in the air in the cafeteria, and how working out the relation between the spin rate and the precession rate ...
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### Are these equations correct for the motion of a gyroscope?

I was coding a gyroscope simulation and came up with some equations that I used for it. So firstly, torque = (change in angular momentum)/(change in time) = (vertical moment of inertia)(vertical ...
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### How can the expression $\dot{\psi}^2$ be derived? I am able to derive it given the $I_{xx}, I_{yy}, I_{zz}$ moment of inertias, but not for $I_o$

This is the question. Center of mass = $3h/4$ from the tip. Radius of base, $r = h \times tan(\beta)$. $I_{xx} = I_{yy} = 3m(4r^2+h^2)/80, I_{zz} = 3mr^2/10$.
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### Velocity of a point on a rigid body, relative to the center of mass, when the entire body is in a circular orbit

Suppose I have an inertial reference frame centered around the point $O$. At a distance $\vec{R}$ from this point, we have the center of mass of a rigid body. This rigid body is revolving around the ...
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### Doubt in the proof of Euler's rotation theorem

The question arises the way Goldstein proves Euler theorem (3rd Ed pg 156 ) which says: " In three-dimensional space, any displacement of a rigid body such that a point on the rigid body ...
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### Gyroscope Angular Momentum Analysis

I'm puzzled by the following questions on gyroscope in HRK physics 5ed (p. 220) Basically the gravity torque is $~τ=Mg\,L\,\sinθ~$. The angular momentum $L_s=I_s\,ω_s~$ has a horizontal radial ...
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### What is faster? Pure rolling or rolling with slipping?

So we know that a ball will slide down an incline when there is no frictional force. Once you say there is static friction it causes a angular momentum which in turn causes a torque and makes the ball ...
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### Is it possible in principle, to analyze problems in rotational mechanics using force and mass, instead of torque and the moment of inertia?

Suppose we are studying the case of uniform circular motion. The analysis of such motion is usually done using Newton's second law as $ma=m v^2/r$. Even when the motion isn't purely circular, like the ...
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### Transforming Moment of Inertia/Angular Momenta in Lab Frame for Rigid Bodies

This is just a quick question about transforming rigid bodies. Suppose we have a problem where we can find the moment of inertia tensor of some rotating rigid body in the body's frame (take it as ...
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### Tipping of a box being pushed at bottom

In space, a rod being pushed anywhere other than its center of mass will rotate and translate. On the ground, a box being pushed at the top will tip if $$Fh > \frac{mgw}{2}$$ How does the ...
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### Inertia Tensor of an Ellipsoid [closed]

I tried calculating the Inertia Tensor for a symmetric ellipsoid given by the equation; $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$ I had no trouble finding the diagonal elements for ...
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### Why do we use negative mass in this question?

So there is a problem based upon the Center of mass and Moment of Inertia of continuous rigid bodies. So let's say we have a sphere of radius R and its mass is uniform throughout the system of ...
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### When a force acts on an extended object how much of the force goes into linear motion vs rotational motion?

So basically my question is when a force acts on a rigid body I know that the part of the force perpendicular to the rotation axis of the object causes a torque and therefore a rotation (If it is the ...
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### Angular velocity across different reference frames

In classical mechanics: Logically, it appears to me that if I draw a mark on a ball and let it roll, the amount of time that will pass before the mark reaches the same position (in terms of angles: ...
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### What happens if a force is applied to the center of a rod?

Imagine there is a 1d-rod (representing a simple rigid "body") of length L. If we apply a force on the end of the rod it will result in a fast rotation around the rod's center, if we apply ...
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### What force am I feeling when I poke a gyroscope to spin off axis of rotation?

So this question is very simple however there is so much material on gyroscopes that I am getting my wires crossed. What I understand, if you poke a gyroscope it will react 90 degrees in the direction ...
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### Lagrangian and Hamiltonian for classical rigid rotator

Suppose we have an idealized rigid sphere with some (spherically symmetric) charge and mass distribution so that it has isotropic moment of inertia $I$ and gyromagnetic ratio $\gamma$. Suppose further ...
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### What will be the angular velocity of a line about a line that is at some angle with the plane of motion?

In this book it is written that angular velocity of a rigid body is time derivate of "angular displacement" of any line in the plane of motion of the body. The angular position of the line ...
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### What are centripetal forces for flywheel precession movement?

What are centripetal forces for this flywheel? I suppose for rotation around "inner" axis centripetal force is due to attractive forces between particles inside flywheel. However what about ...
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### Particle colliding completely inelastically with a sphere placed on the floor

I'm thinking about the problem of a moving particle colliding completely inelastically with a sphere. The aim is to find the vertical component of velocity of the centre of mass of system after ...
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### Rigorous proof that a net force of zero guarantees zero linear acceleration in rigid bodies

I've never found a rigorous proof of this fact. The center of mass' acceleration is not necessarily the linear acceleration, specially if the body is attached to a pin or another geometric constrain, ...
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### Confusion about friction during pure rolling

Friction comes into play with the relative motion between the surface and the points of the body in contact with it. In a perfectly rolling sphere, the instantaneous velocity of the bottommost point ...
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### What is the effect of a tangential force on a rigid body in terms of kinetic energy? [duplicate]

Let's take into consideration a sphere. We apply a force F tangent to the sphere. We know that the linear acceleration of that sphere will be equal to F/m where m is the total mass of the sphere. Then ...
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### Issue about rotational and translational kinetic energy of a pendulum

Let’s say we have a pendulum that consist of a light string hanging a disk-like object. It is allowed to undergo simple harmonic motion with small oscillations. My question: Is the energy of the disk ...
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### Moment of Inertia of a non-uniform rod about its geometric center

Suppose we have a rod of length $L$, whose mass varies as $kx$ from one of its endpoints. I'm supposed to find the moment of inertia of this rod, and I'm facing a small conceptual problem. If I'm ...
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### Angular momentum of rolling sphere confusion

I was reading about the angular momentum of rigid bodies, and I cam across the following problem. Imagine a solid sphere is rolling down over an inclined plane without slipping, and I was trying to ...
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### Modeling Golf Ball rolling around in golf hole

I am trying to model a rotating/rolling golf ball’s interaction with a golf hole. The boring case is just the ball rebounding in an elastic collision off the wall, with conservation of momentum ...
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### Rolling without slipping, general analysis [closed]

Consider first, the simple case of a disc rolling horizontally on the x-axis, having angular velocity $\mathbf{\omega}$ Let p be any point on the edge of the disc. Let $\mathbf{r_{c}}$ be the ...
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### An application of Torque

When we press an end of a stick/rod against a wall (rough enough to ensure that friction balances the weight) what happens is that owing to friction the point of normal force shifts to prevent ...
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### Conservation of angular momentum - why can't $\textbf{r} \times$ be replaced with arbitrary continuous function?

None of Newton's laws of motion, directly states the conservation of angular momentum. For a point mass it's obvious and can be derived from momentum conservation just by taking the cross product with ...
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### Are rigid body collisions elastic or inelastic?

Suppose two rigid bodies collide head-on in a vacuum. Will the collision be elastic or inelastic? In most rigid body computer systems you have to specificy a coefficient of restitution for the ...
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### Torque from drag force

A diver (assumed to be a rigid body) leaping off the springboard experiences no external torque from gravity since gravity acts at the COM. Air resistance doesn't act on every particle of the diver so ...
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### Angular velocity of a cylinder rolling in another cylinder

I'm having troubles with the following problem: Consider a hollow cylinder of radius $2R$ which has a point of its rim fixed in an inertial frame and can rotate about this fixed point. Inside it there'...
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### How to find angular velocity vector of a three dimensional rigid body given velocity of three non-collinear points on the same?

The position of a three-dimensional rigid body is completely defined by specifying position vectors of three non-collinear points on the body. Similarly, one can define the motion of the rigid body by ...
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I have just recently studied Euler's Equations for Rigid body dynamics. Following through the proofs and equations, there is one thing that I can't seem to make a sense of. in $$\dot{\textbf{L}} + \... 2answers 50 views ### Rigid body motion and perpendicular directions While studying Rotation of Rigid Bodies, I came across the following situation: Consider a rigid body in pure rotational motion about a fixed axis (for example the z-axis). For any particle in the ... 0answers 103 views ### Q: Landau Vol. 3, Section 103 (3rd ed.) Quantization of the rotation of a top Have been reading section 103 of L&L quantum mechanics, and have some problems with understanding/interpretation. Hope someone can help out. In the section it is said that the coordinate system \... 1answer 76 views ### Rigid Body Simulation with Joints I have read the basics of how force based physics simulation works and how you can create joints by enforcing certain constraints on the forces between two rigid bodies. What is unclear to me is what ... 2answers 67 views ### Does angular acceleration depend on the reference point? Assume that we have a free rigid body, its own weight being the only force acting on it. If I want to know its angular acceleration, then I calculate the total moment acting on the body. Now, if I ... 2answers 105 views ### Rigid body mechanics in Arnold's book I'm having some trouble understanding what is going on in Mathematical methods of classical mechanics (Arnold, 2nd edition) in the rigid body mechanics section (chapter 6). I don't know any other book ... 0answers 22 views ### Global parametrization of configuration manifold Let's consider a sistem of N material points whose positions x = (x_1,\cdots,x_N)\in \mathbb{R}^{3N} are costrainted for every t to lie in$$C_t = \{x \in \mathbb{R}^{3N} : \psi(x,t) = 0\} ...
Let me explain my doubt with help of an example consider a disc of radius $2R$ rotating with contant angular velocity $\omega$ locate two particles $A$ at a distance $R$ from centre and $B$ at a ...