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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115 views

Forces that exert torque on a rigid body in rotation when angular momentum is not parallel to angular velocity

I'm confused about the rotation of a rigid body, when the angular momentum $\vec{L}$ is not parallel to the angular velocity $\vec{\omega}$. Consider a barbell with two equal masses that rotates ...
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2answers
93 views

Rotational work and forces such as static friction or ropes tension

I'm confused about the rotational work, defined as $W=\int_{\theta_1}^{\theta_2} \tau_z d \theta $ Where $\tau_z$ is the component of the torque parallel to the axis of rotation $z$. Consider a ...
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1answer
47 views

What is the relationship between $W_1$ and $W_2$? [closed]

I have a model which schematic is in the linked picture. Blue $A$ and $B$ are rotational joints, black and red shapes are rigid elements. $I_1$ is moment of inertia of black and red elements combined ...
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2answers
72 views

Does Angular Momentum change what I change Center Of Mass?

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
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1answer
52 views

Does the rotational form of Newton's second law always hold?

Does the equation, $$\vec \tau=I\vec \alpha$$ (rotational form of the second law) always hold? If not, in what conditions does it hold true?
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2answers
81 views

Why does a bowling ball hook in the shape of a parabola?

As an aspiring professional bowler, I'm attempting to understand all the factors that influence a bowling ball motion. The simplest case is when the bowling ball is a uniform sphere and the center of ...
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0answers
44 views

What causing the axis of rotation of a bowling ball to change

A bowler throw a bowling ball with an initial velocity and initial rotation. Let the initial velocity vector be parallel to the y-axis. Now, the ball is rotating about an axis, call that the axis of ...
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1answer
73 views

Rigid body motion degrees of freedom

A rigid body moving in $\mathbb{R^2}$ has 3 degrees of freedom and in $\mathbb{R^3}$ has 6 degrees of freedom. Could you please help me show that a rigid body moving in $\mathbb{R^n}$ has $\frac{n+n^2}...
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0answers
80 views

Why did Einstein allow unphysical objects in his 1906 paper on $E=mc^2$?

In the first part of this paper, Einstein considers a "rigid cylinder", "massless cavity", as well as a "massless carrier mechanism" that is used to transport the massless cavity. These hypothetical ...
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0answers
26 views

Relative velocity of the center of mass in a rotating coordinate system

Say I have a rigid body in space. Let k be a stationary coordinate system, K a coordinate system rotating together with the rigid body, so the transformation $B:k \rightarrow K$ it's just a simple ...
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1answer
39 views

Which force acts as centripetal force on gyroscope?

I think I have understood gyroscope in terms of angular momentum and how the torque of gravitational force moves it the way it does. Also I understand the direction in which it would move: What ...
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1answer
48 views

Rigid bodies and inelastic collision

If two rigid bodies collide - how the collision can be inelastic? where the energy goes? If the energy transffered to heat, doesn't it contradict that the bodies are rigid?
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0answers
15 views

Understanding the inertia matrix of a tilted ellipse

I would like to control the rotation of an ellipse which is tilted by 45° with respect to the rotation axis, and I need to calculate the inertia of the load on the shaft. To be clear, on this figure I ...
5
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1answer
106 views

Why doesn't the 9th ball move in the break in the nine-ball pool game?

In the game of nine-ball pool, we break the rack like shown below: In the break, we hit the 1st ball with the cue ball. Many people familiar with pool games say that if the rack is constructed ...
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0answers
33 views

Rotating disk moving on a circular path

A uniform disk with radius $R$ and mass $M$ is in earth's gravitational field (i.e $\vec{g}$). A point $A$ on the perimeter of the disk is attached to a circular path with radius $L$, and the disk is ...
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2answers
58 views

Why does an ice hockey stick, when thrown on ice always rotate and translate together before coming to rest? Why not only rotate or only translate?

When a hockey stick is thrown on ice it simultaneously rotates and translates before stopping. Friction probably plays the main role here, along with the shape of the stick. I think maybe it is due to ...
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0answers
45 views

Conservative/Non-conservative nature of hinge force [closed]

Can total mechanical energy be conserved for a hinged rod free to move in the $X-Y$ plane? Because, there's the hinge force. If it is non-conservative, energy won't be conserved. Is it conservative?
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1answer
67 views

Moment of inertia meaning?

Why is the formula for calculating the moment of inertia this integral $$ \int r^2 dm~? $$ I understand the way we derived this formula from looking at the distribution of kinetic energy of a ...
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2answers
250 views

Direction of static friction in inclined rolling motion

I can't seem to understand in which direction static friction faces for inclined plane motion with rolling motion. This considers rolling motion without slipping, how do i find the direction of the ...
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1answer
44 views

Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
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1answer
65 views

How do I handle elastic contacts in a simulation with friction [closed]

I'm trying to simulate a wheel as it hits the ground. Problem 1 Suppose a disc is dropped from a height. It has initial velocity of $-x,-y$ caused by throwing and gravity. It has no initial angular ...
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1answer
33 views

Understanding the constraint of tension with a rigid body

I want to know why doesn't $T_1 = T_2$? I think its probably because of the Pulley but still aren't the Tensions Equal but opposite in direction.
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1answer
115 views

Gyroscope precession

I have a system diagrammed and explained in the image below. Experimentally I believe the wheel will rotate around the pivot point where the cable is attached in a counter-clock motion if ...
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0answers
62 views

How can we solve 2D rigid body collision? [duplicate]

I know that usually collision with velocity collinear can be solved by simultaneous equations of both conservation of energy and linear momentum. But my question is when 2D velocity is encountered, we ...
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1answer
34 views

Why does this consider the center of mass instead of the end? (RIGID BODY MOTION) [closed]

A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end. The rod is released from rest in the horizontal position. What is its angular speed when it ...
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1answer
89 views

Angular momentum of a rigid body about any points

Is angular momentum about all points same if the body is rigid and is rotating/translating/rolling with a constant velocity? Why? No external force is acting on the body.
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1answer
50 views

Angular acceleration of a car door [closed]

http://imgur.com/F3eAF9F Edit: i uploaded to the site but it came out really blurry so heres the imgur link I don't get the solution at all, where does the -ma r cos theta come from? (Sorry on my ...
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4answers
137 views

Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
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1answer
68 views

Tangential Velocity of a Rotating Rod

I have the following question which has given rise to a doubt. One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no resistance. ...
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1answer
74 views

Why do we need theorems like **Parallel Axis Theorem**

In rigid body pure rotation, quantities like $\omega, \tau, L, I, r_i$ (symbol with usual meaning) are axis dependent. Assume rigid body to be sphere rotating about the axis passing trough the center. ...
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0answers
46 views

What is required for a time-varying moment of inertia matrix?

Let me preface this question by stating that I am familiar with euler's equations for rigid body dynamics, torque and angular momentum. Despite the math, I'm still a little fuzzy about certain ...
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0answers
21 views

Equation of motion for rigid T-shaped object

Suppose I have a rigid T-shaped object, that is described by three points $A,B$ and $C$. $A$ and $B$ describe the corners of the "top" of the "T", lets say these have coordinates in 3D of $r_A = (0,0,...
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0answers
73 views

Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
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1answer
78 views

How to set up the Lagrangian for this kind of problem?

I'm currently studying rigid bodies in Goldstein's Classical Mechanics book but although I understand the theory I'm not yet understanding how to set up the Lagrangian in some situations. One such ...
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0answers
94 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
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0answers
24 views

Polygon with moving/rotating vertices (or chained line segments)

Suppose we have a polygon, where vertices are point masses, and rods joining them are massless. Now, we pull one of the vertices, what equations govern the motion. How about if instead of a polygon we ...
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1answer
337 views

Intuitive Explanation of Tippe Top Effect?

A friend showed me a tippe top (a special kind of spinning top) lately and asked me about the physics behind it. I thought about it for a while but cannot quite figure it out. So I will throw the ...
0
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1answer
36 views

Formula for speed of rigidly connected objects with one “turning off” of the line?

In the diagram below I have two objects traveling up the diagram on the black track at some speed s, separated by distance D connected by a breakable rigid rod. Further along the straight-line track, ...
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2answers
81 views

Configuration manifold of a rigid body

As I know, a rigid body is a set of $N$ particles in three-dimensional space subject to the following constraint: if $b_1,\dots,b_N\in \mathbb{R}^3$ are the initial positions of the particles and if $...
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0answers
26 views

Rotational Velocity

I would like to calculate rotational velocity from Global(fixed frame of reference) in local (moving frame of reference). How to do that? i know the relationship between global and local frame of ...
5
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2answers
487 views

How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
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1answer
55 views

Will a coin topple if the center of the coin is just on the corner of the square table?

3/4th of the coin is outside the table and 1/4th is on the inside. Also assume that the center of the coin is just on the inside.
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1answer
43 views

How does axial offset effect rotor balance?

I have a thin rod rotating about its primary axis, rigidly attached to mass $m_1$ whose center sits at distance $r_1$ from the axis and position $y_1$ along the axis. $m_1$ exerts a centripetal force ...
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2answers
75 views

Rod partially handing off edge of table

A uniform rigid rod of length $L$ lies at the edge of a frictionless table so length $x$ of the rod rests on the table and the rest is beyond its edge. Intuition suggests that the rod will stay like ...
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1answer
95 views

Transform velocities from one frame to an other within a rigid body

I come from non-physics background but just came to face the following problem. I have a rigid body with two attached frames of reference A and A'. I know: the rotation and translation between A ...
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1answer
88 views

When we ride a bicycle, why do we tend to move left when we turn it right? [duplicate]

When we ride a bicycle, we tend to move our body left if we are taking a right turn and vice versa. Why is it like that?
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0answers
64 views

Why is this handle flipping back and forth? [duplicate]

This gif of some kind of handle being spun in zero gravity has been doing the rounds: Why is it flipping back and forth? It seems odd that it flips, then seems to rotate around one axis in a ...
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0answers
87 views

Rotational dynamics equation for a variable mass system?

I'm searching for the formulation of Euler's rigid body dynamics in the case of a variable mass system. I'm reading the book Mechanics of Flight by Warren F. Phillips (2nd edition) and unfortunately ...
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1answer
182 views

Kinematics of Euler angles relative to a rotating frame

I have a rotating body $B$ and a rotating frame $F$ whose orientations are described by the quaternions $q_B$ and $q_F$ respectively. I also have the angular velocity vectors $\omega_B$ and $\omega_F$....
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1answer
53 views

'Eulerian' description of a rigid body submerged in fluid

In this paper, equations of rigid body motion (eq 4 and 5 in the paper) are written in Eulerian form (eq 12 in the paper). The rigid body is submerged in a viscous incompressible fluid. $$m\frac{dw_G(...