# 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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### Would a homogeneous rod on a fulcrum oscillate or remain at rest after displacement?

If I take a homogeneous rod, put it on a fulcrum, push one side down in a controlled way and release very carefully won't the rod just stay at rest in that new position? ChatGPT says that it would ...
1 vote
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### If the net external moment on a body about a point is zero

I was told that If net external moment of some forces is zero about a point, then the net external force passes through the point. I know it's not true in general, what was the special condition ...
59 views

### Do off-centre forces create additional energy?

When a force is applied to a rigid body at its centre of mass, it accelerates. Over time, that acceleration becomes velocity, which gives the body a certain amount of kinetic energy. However, if that ...
326 views

### What is the moment acceleration of the center of mass for a rigid body under an external force

As shown in the following, a rigid body experiences an external force $\overrightarrow{F}$ away from its center of mass C: The rigid body is assumed to be free in space, experiencing no other force. ...
1 vote
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### Why don't Euler's formulas for torque apply to this problem?

In my mechanics class we were assigned problem 9.44 from "Introduction to Classical Mechanics" by David Morin as homework. The problem and figure are below: Two wheels of mass $m$ and ...
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### Gyroscopic effect of a sphere

I am looking at: https://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics) \begin{align} I_1\dot{\omega}_{1}+(I_3-I_2)\omega_2\omega_3 &= M_{1}\\ I_2\dot{\omega}_{2}+(I_1-I_3)\...
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### Motion of bowling ball

I'd like to model the motion of an asymmetric bowling ball thrown on a bowling lane. I know there's forward momentum and angular momentum that moment the ball is released, and there's of course ...
284 views

### What is the physical significance of Moment of Ineria about a point vs Moment of Inertia about an axis. In which types of problems we use the former?

I know the mathematical formula of both about an axis and a point. But where exactly we use moment of Inertia about a point. For 2d objects like discs rotating in its own plane, the moment of Inertia ...
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### Angular Velocity of 3D object rotating in space

For a sphere rotating about z axis, its angular velocity is rate of change of angle of a radius vector in xy plane with x axis or y axis. I understand this clearly. But consider a 3d body which is not ...
251 views

### How to apply a screw motion for this case?

I'm completely new to the notion of a screw motion. As far as I know, it carries out the the rotation and translation simultaneously in comparison with the homogenous transformation matrix that ...
1 vote
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### Why isnt the contact force between the rack and wheel 200N?

I was looking at this YouTube video 'Example 1' (from 4:17 timepoint) and wondering why the contact force F between the rack and wheel isn't also 200N? Isn't this constant force of 200N being ...
1 vote
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### Question on rotational dynamics

My book states that it's convienient to apply torque equation $\tau=I \alpha$ on instantaneous axis of rotation and centre of mass. My question is: why it is so? And how can we apply torque equation ...
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### Torque about an axis for an object [duplicate]

Suppose I have an object-(a disc for example), it is rotating about all of its 3 principle axes with some angular velocities .Along with that, the principle axes are also rotating, giving an extra ...
353 views

### Motion of a point on a rotating rigid body in three dimensions

Let $\mathbf{p}$ denote a point on a three-dimensional rotating rigid body, and consider a body-fixed frame of coordinates centered on $\mathbf{p}$ rotating with the body. Assume that the body is ...
247 views

### Confusion regarding derivation of euler's equation

I'm having confusion regarding the derivation of Euler's equation for rigid bodies. Suppose I have an inertial frame $O$, and a rotating frame $O'$ fixed to the rotating body and the rotating frame ...
445 views

### Confusion about angular momentum of rigid bodies

I know that angular momentum of a rigid body has a parallel and perpendicular component to the angular velocity. I also know that the perpendicular component is due to constraints that keep the axis ...
1 vote
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### Rotation axis for angular momentum and torque formulae to be valid

My current understanding of angular momentum and torques are that they are both defined for an arbitrary point, $o$, (pick the point and calculate, different points can have different values) and the ...
1 vote
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### Is the idea of a rigid body compatible with Newtonian mechanics?

It is known that rigid bodies cannot exist in the framework of special relativity by causality arguments. But recently I saw a video on YouTube that claims rigid bodies are not compatible with ...
1 vote
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### Evolution of rigid body system using Impulse Based integration [closed]

I have been reading about physics engines, I have a reasonably OK understanding force based models and 6 dof integration. I'm still confused on how impulse based models work. What define the equations ...
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### How can precession produce a torque in the direction of precession when it has no angular momentum?

Updated question, also includes somewhat of an answer. To clarify the point about precession having no angular momentum, if the torque that induces precession is suddenly removed, the gyro suddenly ...
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### Can torques cause both transitional and rotatory motion?

Imagine a rod (a rigid body) 10 meters long that is freely floating in space without being attached at any point. Its mass is 12 kilograms and according to most sources I found, its moment of inertia ...
168 views

### Why can't rotations in general be associated with vectors?

In my textbook, there's a question: A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be ...
1 vote
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### Gyroscope precession and Euler equations

I've been trying for so long to solve this problem, but the solution I have found isn't the one I expected. Basically, I have to solve Euler's equations for a gyroscope with a weigth at a distance d. ...
496 views

### If torque is the driver of rotation, why doesn't more torque (rotational force) mean faster rotation?

I got confused about the car. In most places they said that for acceleration when we start we need more torque (which is consistent with the fact that the highest acceleration is in first gear). But ...
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### How to compute inertia tensor off the center of mass with geometric algebra?

I was reading Doran & Lasenby's Geometric Algebra for Physicists when I stumbled upon this, where $\mathbf{a}$ is a vector taken form the centre of mass. Returning to the definition of equation (...
936 views

### Rotational kinetic energy of rigid bar

Consider a rigid bar (infinitely thin and with uniform mass density) of length $L$ with $x_1(t), x_2(t) \in \mathbb{R}^3$ each describing the positions of an endpoint of the bar in some fixed inertial ...
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### Why can any general motion of a rigid body be represented as translation + rotation about center of mass?

Why can any general motion of a rigid body be represented as translation + rotation about center of mass? I am beginning to read rotational dynamics and my textbook states this fact without proof. I ...
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### Difference between the case where net force is zero and when no force is acting

I read online that the difference between the two cases is that the body deforms, but what if the body is perfectly rigid would there be another way to diffrentiate between the two cases? if not then ...
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### Does the direction of an angular velocity vector always stays constant with no force involved [duplicate]

Are there cases where there is a rigid body that rotates somehow and the direction of the angular velocity vector changes in the lab system?
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### Is energy conserved on a ball sliding without friction?

If a ball is sliding without friction (down an inclined surface) is energy conserved? I can’t think of why it wouldn’t be, but my intuition on this stuff is really bad.
1 vote
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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 ...
1k views

### Energy conservation for a rolling rigid body

I came across this question where A solid cylindrical body of mass m and radius r rolls without slipping over a smooth inclined plane. Its initial velocity is v. What would be the maximum height ...
43 views

### Torque at only two points of contact between a rope and a disk (rigid body dynamic)

In physics, particularly when dealing with rigid bodies, there's a common practice of calculating torque at only two points of contact between a rope and a rotating disk, typically at the extremes ...
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### Is this the correct way to integrate orientation given torque and inertia tensor?

I am trying to develop a 3D rigid body simulation in C++ in which I had some conceptual doubts on how to integrate for orientation given the total torque applied to a rigid body, and it's initial ...