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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Doubt in derivation of bending of beam, It's about derivatives and intergration

Radius of curvature of the beam in above picture is given as: $$ \frac{1}{R} = \frac{d^2 y}{dx^2}$$ Please help me two points used as steps of a derivation in my book: How was the radius of ...
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Angular Momentum of asymmetric physical pendulum (Rigid Body)

The angular momentum of a rigid body respect to a pole $O$ located on its axis of rotation $z$ is uniquely determined if we know its angular velocity: $\vec{L}_O = I_z\vec{\omega} - \omega\iiint_V ...
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How would a rigid disk rotating near speed of light behave? [duplicate]

Say you had a perfectly rigid disk so that you can't morph it or bend it. If you were to spin near the center of the disk at near speed of light, the edge of disk would have to be faster but of course ...
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Will the puck rotate without slipping in this situation?

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 ...
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Using matlab to simulate a spinning top [closed]

The hamilton equation of inclined angle theta of a spinning top is written in Classical mechanics Kibble 5th edition p.285 (https://physicaeducator.files.wordpress.com/2018/02/classical-mechanics-by-...
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Angular velocity of point on rigid body [duplicate]

a while back I asked this question and I still did not fully understand. Suppose we have a rigid object rotating about some central point with a given linear and angular velocity, how do we then ...
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Number of Degrees of Freedom of a Rigid Body System - Proof

Let us define the number of degrees of freedom of a material system as the number of scalar parameters needed to know the position of each particle of the system with respect to any inertial frame of ...
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Doubt in Equations of motion of rigid body, can anyone tell me how the second step occurred from first one [closed]

Doubt in Equations of motion of rigid body, can anyone tell me how the second step occurred from first one.
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Conservation of energy in a rigid body

"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. The other end of the rod is held still so that it touches the ...
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5 answers
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Is work done by torque due to friction in pure rolling?

This question has been asked and answered numerous times. I went through almost all of them and found no consensus. I found that all of the answers can be divided into two categories: Friction does ...
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Euler's Angles and Uniquely Defining the Orientation of a Rigid Body

When speaking about the orientation of a rigid body, Symon (Mechanics, 3rd ed.) writes: It turns out that no simple symmetric set of coordinates can be found to describe the orientation of a body, ...
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How do the inertia tensor varies when a rigid body rotates in space?

The inertia tensor is clearly constant the in a frame moving with the rigid body. But what is the simplest way to see why its columns can be considered rotating vectors in space with the angular ...
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When two systems of forces acting on a rigid body are equivalent?

My book says that "it is clear that if you replace the system of forces with a second system having the same resulting force and the same resulting moment, with the same initial conditions the ...
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Does an irregular rigid body can only rotate in three directions?

Suppose that at a certain instant the angular momentum with respect to the center of mass is not parallel to the angular velocity. Does this necessarily imply that the angular momentum is rotating ...
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Moment of Inertia of a solid hemisphere. What am I doing wrong? [closed]

I want to calculate the MOI of a uniform solid hemisphere about Axis passing through its centre of mass (COM) and perpendicular to the circular base. Axis coinciding with any diameter at the ...
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What is the angular momentum of a particle rotating around an axis in 3D?

What would be the angular momentum of the particle at position $r_i$ in the diagram above? The vector from the axis of rotation is $R_i$ and the tangential velocity is $v_i$ so the magnitude of ...
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How does Schwarzschild spacetime bend a free falling rigid body?

How does Schwarzschild space-time bend a free falling rigid body? Will it be stretched or squeezed? How much it will be modified? Can we find an effect of Lorentz contraction? When will the assumption ...
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Why is the sum of torques for each particle equal to the external torque?

Let's assume we have a rigid body. The internal forces all have equal and opposite counterparts so the they will produce a net zero torque. We can therefore ignore internal forces when calculating the ...
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How can the total torque of a body equal a "torque" at only one point?

I am trying to understand the solution to this problem. Pictured is a rough sketch of a ball in which another, smaller ball of density $\rho_2 > \rho_1$, where $\rho_1$ is the density of the ...
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Rotational frames and Coriolis deviation

I have a question regarding a problem that is the deviation of an object due to the rotation of the earth ( cause by pseudoforces ). I've seen this video on youtube https://www.youtube.com/watch?v=...
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Inertia tensor for rotors

For vectors we can use Inertia tensor. But if I want to use bivectors (Rotors), what should I use for the inertia tensor? I want to make a 2d game and progressively to 4d.
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Do Newton's laws of motion apply on rigid bodies?

If they apply on rigid bodies, would we consider forces acting in any direction or on any part of the body, and consider only the centre of mass when we talk about its momentum or the body being at ...
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Does the character of the body, ex. symmetrical top, sphrical top, depend on the origin chosen?

Given a homogenous cube of length b and mass M. If we start with one of the vertex being the origin then the inertial tensor in this case is $$ \{\textbf{I}\}=\begin{Bmatrix} \frac{2}{3}\beta & -\...
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Acceleration of an instantaneous centre is always 0? [closed]

I came across the following question recently: My understanding of the question is that it wants us to show that end A is an instantaneous centre. The mark scheme does so by showing that A has no ...
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Quadcopter motor speed mixing

I'm having trouble solving the following problem. I've designed a control system for a quadcopter, my design is built upon a nonlinear model in the affine form: $$ \dot{x}=f(x)+g(x)u $$ The system ...
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Which frame to choose for these equations of motion?

I have a robot with four wheels and I want to create a model to simulate its movement (in the plane). Assume the robot is a perfect square with side length 1 and wheels at its edges: ...
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7 votes
2 answers
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On the motivation of definition of angular momentum

As the title asks, what is the motivation for the definition of angular momentum and by extension torque? In all the books, be it of undergrad or grad, the definition of the above mentioned is just ...
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How are rigid solids approached in the context of Lagrangian formalism?

Maybe it's my own fault, but neither in my classical mechanics class nor within any book I've read on the subject I have found an extensive use of analytical mechanics to discuss the motion of solids. ...
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How to find inertia tensor of a circular ring from angular momentum and velocity?

Consider a thin circular ring with radius $R$ and axis of rotation as shown in the figure. If $\vec{L}$ denotes angular momentum and $\vec{w}$ is the angular velocity then $$\vec{L}=\begin{bmatrix} I_{...
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Why is the force on a rigid pendulum directed radially?

Consider a typical presentation of a simple pendulum: a point mass $m$ attached to a rigid rod of length $L$, which is free to rotate around a pivot. Newton's equations are $$\begin{gather} mg \cos\...
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How much degree of freedom of a rigid body in $N$-dimensional space?

Well I have the answer it is $\frac{N(N+1)}{2}$ but what the procedure to derive it . I tried this. 1).I have $N$ number of translation freedom. To calculate the number of rotational freedom I tried ...
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Resource recommendation for rigid body dynamics [duplicate]

I want a book at undergrad level that teaches rigid body dynamics from a physical perspective, that is explaining the need for each term introduced, instead of saying "this is a term which is ...
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Stress in a rigid body

Consider two bars one rigid and the other deformable, acted upon by two equal and opposite point loads P as shown. In either of the cases, if we cut the beam from an imaginary section, then, to bring (...
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1 answer
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Distribution of contact forces on a square at rest

Consider a square (blue) on top of a platform (yellow), on which gravitational force (black) acts. We know that if the blue square is in equilibrium, contact forces from the platform (white) must act ...
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Torque on a rod in a harmonic potential

I'm trying to find an expression for the force and torque on a rod in 2D subject to an external harmonic potential \begin{equation} V = \frac{k}{2}x^2 \end{equation} I know that the force on the ...
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Moment of Inertia of a Rectangular Parallelepiped

Moment of inertia calculated about an edge for a rectangular parallelepiped is given by $$I = (m/3) (a^2 + b^2), $$ my question is: when m(a^2+b^2) is added to I, the new value obtained is Moment of ...
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3 votes
5 answers
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Why do objects with lower rotational inertia have more translational kinetic energy?

In my physics class, we have seen experimentally that objects with lower $I$ values (like spheres) will reach the bottom of a ramp sooner and with a higher final velocity than objects with higher $I$ ...
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Is it possible to model the rotation of a bowl as a function of time?

I was watching a video where someone spun a bowl, and then let it rotate until it eventually stopped and fell flat onto the table. I was wondering if it is possible to model the rotation of a bowl as ...
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How long would it take for the moon to disintegrate into a ring if placed inside the Earth's Roche limit?

Wikipedia says the Earth-Moon rigid Roche limit is about 9500 km. The moon's diameter is roughly 3500 km, so say I magically teleport the moon to within 6000 km of the Earth—it's fully contained ...
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Moments of inertia

I know the concept of moment of inertia from $L=I \omega$, $\tau =I \alpha$, $I=mr^2$, and so on. I also know the that, in general, $I=\int r^2dm$ I would like to know how we derived the moments of ...
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3 answers
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Does moment of inertia tensor keeps changing if object is rotating about multiple axes?

Consider a plane circular disc kept in X-Y plane with Z axis passing through its centre. It is rotated about all threes axes with some angular velocities. In such a case, to find the inertia tensor, ...
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Why a rotating body ruptures at a transverse velocity equal to the speed of sound in the body?

In this article about Ehrenfest's paradox, an introductory remark on classical rigidity is made: Any rigid object made from real materials that is rotating with a transverse velocity close to the ...
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Mixing position and force based simulation

I have read quite a bit on rigid body physics engines and feel I have a reasonable understanding of how systems evolve with force based simulation. What I am kind of confused on still is how you mix ...
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Relative angular velocity and linear acceleration of a fixed rigid body coordinate with respect to another moving rigid body coordinate

Let me describe a problem I currently have: The robot (orange box) moves around the object (green box) located in a fixed position. Odom keeps providing a homogeneous transformation (rotation and ...
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2 answers
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Question about Rotational Kinematics in David Tong's Notes

In the $2$nd page here of David Tong's notes on the Motion of Rigid Bodies, at the bottom there is a claim about the unique existence of a certain time-dependent orthonormal matrix $R(t)$ whose $9$ ...
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2 answers
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Does moment of inertia has to be with respect to a rotational axis?

Say we have a disc with its center at the origin. The disc has a mass M and a radius R, the density distribution of the disc is constant and is spinning as shown. The moment of inertia with respect to ...
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Dynamics of interconnected rigid bodies using Newtonian physics

Passive SONAR uses a towed array system to hear the underwater sound uninterrupted. This towed array sonar is a system of hydrophones towed behind a submarine or a surface ship on a cable. The ...
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Frictional wheels without slipping (gear system)

In the figure below it is stated that the friction force should always be greater than the tangential force in order to prevent slipping between two frictional wheels. My question is that if we apply ...
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2 votes
2 answers
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Is torque dependent on the moment of inertia?

I think this is why more force is required for a shorter distance; the inertia causes the object to stop, and greater force is required to cover the angular displacement.
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Kinetic energy of rigid bodies about the center of mass

Suppose, we have some rigid body, that is rotating about some pivot. In this case, we can easily find the kinetic energy, by choosing a random point $P$ on the body. The kinetic energy of the body ( ...
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