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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How to figure out the distribution of Normal Force on a body?

I was solving a problem and came across some confusion. In Classical Mechanics 101, we have always treated the Normal Force as acting on a point, and it was calculated by applying Newton's Laws (...
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Kinematics of a Rigid Body; Thin plate rotated about a point

I need help with this setting up this equation. So far I have after taking the moment about $O$: $$100(1-e^{-0.4t})-0.75mg\sin{\theta}= \left[\left(\frac{1}{12}m(l^{2}+l^{2})\right)+md^{2}\right]\...
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0answers
41 views

How does friction cause a spinning top to fall?

I am wondering how friction can create a torque to change the angular momentum and cause a spinning top to tilt, like in the diagram of a close up of the rounded tip of a top while the angular ...
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What are the limits of spin speed on a graphene ribbon?

In my previous question, link below, I asked what are the limitations on spinning an object with the goal of achieving relativistic speeds at the edge of the spinning object. In the comments, someone ...
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1answer
100 views

Rigid body dynamics: modelling a polygon bounce off ground

I'm currently making a physics simulator, but I'm having some trouble making a polygon bounce off the floor. I know that collisions are normally modeled as described below by ja72, but I did it ...
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1answer
144 views

Does an asymmetric top return to its initial position &orientation, while rotating freely in space? (contradiction in Landau&Lifshitz mechanics book)

The Poinsot's ellipsoid tells us that the angular momentum ($M$) (in the rotating frame) should be lying on the intersection curve between the conservation of momentum sphere radius $|M|$: $M_1^2 + ...
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3answers
136 views

Is flipping a coin is a stable rotation?

If I rotate a coin with dimensions: 10X10X1 about 1 of the big axes(10) in space, where there is no torque, will the rotation will be stable just like a frisbee or a football regular rotations are? ...
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1answer
93 views

Balance of a rolling coin

If we place a typical coin on a table, it will almost immediately fall due to gravity. However, with a little push it will roll and not fall anymore until friction eventually slows it down enough to ...
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How many illusionary axes of rotation can coexist?

Consider the answer to this question: How many different axes of rotation can coexist? Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation. Now, that ...
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1answer
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Rigidity or Bodies with Triangular Shapes of Faces

Originally I read an answer on Quora wherein the author showed that by using magnets he made different shapes. Squares were easily deformed, so we're other shapes with square faces such as cubes ...
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1answer
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Does asymmetric rigid body experience torque-free precession?

I know that a top (or any axis symmetric body) experience torque-free precession. and I know that asymmetric body, with 3 different dimensions has stable rotation when the angular velocity is near the ...
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Finding the total rotation about an arbitrary axis

I have a rigid body which is fixed in a x,y,z system and is free to rotate. The z vector is parallel to gravity. x and y are arbitrary and perpendicular to z. The moving coordinate system is x',y',z' ...
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1answer
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Why conserve angular momentum about COM

In many questions involving collisions between Rigid bodies angular momentum is conserved about center of mass If bodies stick together after collision they estimate com and then conserve about ...
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2answers
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What are the possible method to simulate the dynamics of rigid bodies in simulation? [closed]

I just want to know the name of the methods, the simulation physicist uses to simulate the dynamics of rigid bodies. Eg. Impulse Based Dynamics developed by Mirtich
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1answer
41 views

Rotation of a rigid body within another orbiting body [closed]

I would like to understand the physical behaviour of the following rotating sytstem. There are 3 rigid bodies (1 is blue, 2 are red). We assume that there is no friction between the blu body and the ...
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Accion response calculation on tilt steering kick board scooter

Hi I am designing a home made kick board scooter, need to understant the behaviour between the board angle and the turn angle. In a classic sakateboard the foot action is transformed to turn angle, ...
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3answers
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Z-shaped lever balance

The goal is to find out whether a Z-shaped lever will fall over due to gravity. See diagram below (sorry for MS Paint): The bottom edge $x$ is resting on a flat surface. All three edges, $x$, $y$, ...
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Degrees of freedom [duplicate]

Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space. In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$ ...
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5answers
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Rolling object not stopping even when friction is considered

I am dealing with a question that has me puzzled. Suppose an object which is rolling on a horizontal plane, with initial linear velocity $v=v_0$ and angular velocity $\Omega=\Omega_0$. There is ...
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21 views

Derivation of Equation of motion from Euler-Lagrange Equation [duplicate]

Hello I am new to Lagrange's dynamics and have some doubts regarding derivation of equation of motion given in a text : Deriving Equation of motion for a free body(no-external forces) ,in one ...
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1answer
52 views

Nutation frequency for a weighted gyroscope

So, I've been led to believe that the frequency of nutation of a gyroscope can be calculated using the formula In which the I's are the moments of inertia around the principal axes and omega-3 is the ...
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1answer
55 views

Ideal geometry for a shaft terminating thrust bearing

Following this PyDy example, I'm trying to understand the problem set 3.10 of the book: Kane, Thomas R., and David A. Levinson. Dynamics, theory and applications. McGraw Hill, 1985. page 272 (292 ...
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65 views

If there was no friction would a thin rectangle with mass $m$ with sides $a$ and $b$ spin indefinitely about an axis through its diagonal?

I would like a geometrical physics answers so I can have an intuitive grasp about the problem. That means no nonphysical things like matrices, coordinates and random basis of vectors. For example it ...
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0answers
290 views

Newton's second law in angular form [duplicate]

I'm rather confused about the correct form of Newton's second law in angular form and how matrices of inertia could be converted from one coordinate system to the other. Consider the system below: ...
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2answers
65 views

Angular velocity of rotating rod

Consider the following system: Newton's second law for rotational motion: \begin{equation}\tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{...
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Is it possible to find the linear and angular forces?

Suppose an object has both linear an angular motion. Let's consider the object a sphere. What we know: - The angular velocity and acceleration - The linear acceleration of the center of mass. - The ...
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29 views

Euler Lagrange 2D equation of motion of flying object with inverted $z$-axis

I have the following 2d problem. A flying object of mass M carrying a rigid cable of length L with an attached mass (m) at the end, is described by the following scheme: With $\alpha$ the angle ...
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28 views

Conservation of Angular Momentum about the Instantaneous centre of rotation

While solving some problems on rotational kinematics involving ,say, a cylinder rolling without slipping against a rough surface, I used conservation of angular momentum about the instantaneous centre ...
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0answers
34 views

Factors effecting the time period of Euler's disk [closed]

I wish to carry out research on the factors effecting the time period of a spinning Euler's disk. Do factors like friction coefficient of the base or concavity of the base effect the disk? If not, ...
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1answer
24 views

Parallel axis theorem of stick-ball configuration

I have a system with a rod of mass m and length 2a. Let the origin be in the middle of the rod at x = 0. (Therefore, each end is a distance a away.) A ball of mass m is attached to the far right end. ...
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Insufficiency of Newton's third law to solve constrained motion problems

In The Variational Principles of Mechanics Lanczos describes what he calls 'vectorial mechanics': the process of solving mechanical problems by recourse to the immediate consequences of Newton's laws, ...
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1answer
44 views

Rigid body in a force vector field

If I let a particle with coordinates $x(t)$ move in a force vector field $F$ the equation I have to solve is $x'(t) = F(x(t))$, right? But if, instead of a particle, I have a rigid body, which ...
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1answer
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Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
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How a stick in space moves when force only acts on one end? (suppose stick is rigid body)

I am confused with how to put inertia in to this problem, which suggests the end the force acts on should move first while another end remains fixed at first moment. I think that the stick should ...
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1answer
84 views

Rotation matrix - levi-civita symbol

I'm trying to solve the following problem: Given a rotation matrix $R_{ij}$, show that $$n_k=\frac{-R_{ij}\epsilon_{ijk}}{\sqrt{(3-tr(R))(1+tr(R))}}$$ and that $$\sin(\phi)=-\frac{\epsilon_{ijk}...
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1answer
55 views

Kinetic energy of a yoyo

Consider the yoyo above: The yoyo is constructed from two heavy disks of radius R connected by a light axle of radius r , as shown in the figure below. The total mass of the yoyo is M and its moment ...
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124 views

How to calculate the viscous damping coefficient of a viscous layer between an inner sphere and an enclosing outer sphere?

In this article by Rahn and Barba, a flat-spin transition manoeuvre is investigated. For this it is assumed that a rigid spacecraft contains a spherical, dissipative fuel slug of inertia $\boldsymbol{...
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0answers
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What is centre of rotation and a ref. point fixed wrt to the body?

I'm studying Analytical Mechanics, and in the section about the kinematics of rigid body, it is mentioned the following concepts: Center of rotation a reference position that is fixed with ...
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1answer
23 views

Effect of spin on the deflection of a rigid body

Suppose an x-y coordinate axes is set on the ground, then a spherical object is projected in the forward direction (the positive y direction) and while moving in this forward direction it also ...
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2answers
113 views

Rigid body dynamics derivation from Newton's laws for higher dimensions

Since Newton's laws are defined for point particles, I'd like to derive some laws of motions for rigid bodies only by considering a rigid body as a system of particles such that the distances from ...
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0answers
40 views

Torque from Newton’s Laws

Is is possible to predict the motion of rigid bodies only in terms of Newton’s laws of motion without torque (for example by using the system of particles model)? For instance, if there was a rod of ...
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4answers
218 views

Helical motion of a rigid body

I want to show that a rigid body, with two components of its angular velocity vector and one component of its linear velocity vector, in the absence of external forces and torques, has helical ...
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3answers
60 views

What is the equation descriping a ball motion caused by non-perpendicular force?

What is the equation describing a ball motion caused by non-perpendicular force? For example in the next diagram F1 is perpendicular force but f2 is non-perpendicular force which I am asking about
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1answer
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Angular Momentum and assymetric axis

The question I came across , If a semicircular disc rotates uniformly (const. angular velocity) about an axis passing through its Centre of mass , and prependicular to its plane , do we need an ...
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0answers
26 views

Goldstein expression derivation (Torque-free Motion of a Rigid Body)

In page 207 of Goldstein's "Classical Mechanics" (3rd edition) he writes the following expressions: I can't fully grasp how he was able to get to these expressions. I believe it has something to do ...
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1answer
88 views

How does tension work for a simple pendulum? What force is at play to keep a rigid body from stretching?

Here recently I have been working on programming a physics framework for simulations, but I've ran into a problem... I was testing forces, so I created a simple pendulum like in the photo, and I ...
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1answer
26 views

Directional cosines and rigid bodies

Suppose $Oxyz$ is fixed in space. We specify one reference point in the rigid body using Cartesian coordinates in $Oxyz$. We use this point as the origin of the body-fixed frame $O'x'y'z'$. Consider ...
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1answer
78 views

Addition theorem for angular velocity --> “addition theorem for angles”

I'm wondering if it is possible to go from the addition theorem for angular velocity to the "addition theorem for angles". For example (I used the same notations of Wiki): $${^N\!\omega^B} = {^N\!\...
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Is rigid body mechanics included in classical mechanics?

Can rigid body mechanics be derived from Newtonian, Lagrangian or any other formulation of classical mechanics? Or do we need some extra axioms or laws?
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Is a reference frame fixed (without rotation) on a precessing gyroscope an inertial frame of reference?

Let's say we put a human in a closed chamber which is going around a certain point at distance d from its center of mass at some angular velocity w. The centrifugal force on a human will be w squared ...