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.
862
questions
1
vote
0
answers
36
views
Is Energy conserved in a spinning top?
When we spin a top (give it kinetic energy $K_0$) and place it on a table, it starts precessing around the vertical axis.
Is the total energy of the spinning and precessing top equal to the initial ...
- 1,108
0
votes
0
answers
19
views
Angular Velocity in the Plane of a Lamina
A rigid body (i.e., a 2-dimensional object) has principal moments of inertia about the centre of mass of $I_1 = (\mu^2 -1), I_2 = \mu^2 + 1, I_3 = 2\mu^2.$ I wish to show, using the Euler equations, ...
1
vote
0
answers
74
views
+100
Weird rotational motion of a heavy thick disc
I and my friend noticed a strange behaviour of a rotating disc (or a cylinder) and we don't know how is that happening.
This is the video.
Actually what is happening in the video is that the disc ...
- 7,480
0
votes
1
answer
35
views
Why do we use $\Delta m$ in the derivation of angular momentum of a rigid body?
while I was watching a derivation of angular momentum of a rigid body on youtube, it came to my attention that the person who was doing the derivation, used $\Delta m$. my question is, why did he use ...
- 29
4
votes
2
answers
264
views
Addition of forces on a rigid body instead of a point
When two forces act on a point mass,we add the forces like we usually do and i have no problem understanding that. When the same forces are applied on a rigid body,how are we able to add them the same ...
- 1,011
1
vote
1
answer
44
views
In a rigid body rotating in 3D around the origin, is the norm of the linear velocity of each particle constant?
I was trying to prove that kinetic energy is constant in a rigid body undergoing some arbitrary rotation around the origin in a 3D space, and I ended up proving a stronger statement: that the norm of ...
- 225
1
vote
0
answers
21
views
Is a free rigid body in 3D space an integrable system? [duplicate]
I am trying to find three integrable systems with 6 degrees of freedom using the Liouville–Arnold theorem. That means that a set of integrals of motion that correspond to a conserved quantity for ...
- 11
1
vote
0
answers
57
views
Euler's equation of motion for rigid bodies rotating with one rotation axis not through the body's center of mass [closed]
this is my first question in this forum. Thanks for all the knowledge and support shared throughout the whole website!
I have a body with rotations around 3 axes. I am looking for the external torques ...
- 11
0
votes
1
answer
40
views
How to transform Arbitrary Rotation Matrix $A$ to a coordinate system where the $z$ axis lies along the axis of rotation by Similarity Transformation?
In Chapter 4 of the book Classical Mechanics by Goldstein, it was written that
"By means of some similarity transformation, it is always possible to transform the matrix A to a system of ...
- 135
1
vote
1
answer
48
views
Moment of Inertia of a screw rotating on a horizontal plane [closed]
Since a screw is kinematically equivalent to a cone, you can consider it like one, but I wanted to mathematically model the motion of a screw/cone as it is rotating on a plane. However, the moment of ...
- 23
4
votes
3
answers
205
views
Kinetic energy in combined rotational and translational motion
If a body is free to move I have studied that any point can be assumed to be in translational motion with velocity of the centre of mass along with a pure rotational motion with $\omega$. For Kinetic ...
- 71
4
votes
4
answers
2k
views
How does the parallel axis theorem explain the opening of a door?
As I get closer and closer to the hinges of a door, it becomes harder and harder to open. However, the distance to the hinges is getting smaller and smaller, where the rotation is occurring. All the ...
- 175
1
vote
3
answers
114
views
What illustrative example of the central axis theorm exists? This is not the parallel axis theorem
This is from Ira Freeman's translation of Georg Joos's Theoretical
Physics. I've taken a few liberties with the notation.
It may be shown also that there is always an axis such that if any point ...
- 1,835
-1
votes
4
answers
76
views
Why would a hollow cylinder lose a race with a solid one?
Apart from the physics stuff which clearly shows why the hollow cylinder will lose:
$ T = RF = Iα = I* a/R$, since both F and a are missing we use the second equation F = ma:
Here are the forces ...
0
votes
1
answer
27
views
If torque is not observer dependent for bodies in translational equilibrium then why doesn't the angular acceleration change?
I know that if a body is translational equilibrium then torque about any point is zero and have also understood it's proof. My teacher had told me that angular acceleration about any point will be ...
0
votes
2
answers
35
views
Work of the contact action of a force on a wheel
I have a question regarding wheels.
Suppose I have a skateboard with perfect bearings, and I live in a world without air. At $t=0$, it is on the ground and I give it some initial speed, $\vec{v}_0$. ...
- 5
0
votes
2
answers
63
views
Rolling motion in space [closed]
Is rolling motion possible in space?
If so,
Let's imagine that two cylinders of different masses and inertias were rolled over an incline in space is it the case that the one with lower inertia will ...
0
votes
1
answer
22
views
Center of rotation of a rolling screw
So I was just researching into the motion of a screw as you try to roll it on a surface and I observed that on applying a force/pushing it, the screw moves in a circle like a cone would if you were to ...
- 23
0
votes
0
answers
18
views
Doubt regarding cancellation of internal torque for a rigid body (Kleppner and Kolenkov) [duplicate]
In chapter "Dynamics of fixed axis rotation", the book says newton's laws are not enough to show that the internal torques of a rigid body cancel out.
But section 1.2 in Goldstein says that ...
- 283
1
vote
1
answer
27
views
What does it mean to take a mass moment of inertia about a single point?
This website here: https://www.chegg.com/learn/calculus/calculus/moment-of-inertia-about-the-origin
Shows the following:
How is it possible to define a mass moment of inertia about the origin which ...
4
votes
1
answer
188
views
Ball rolling in a cylindrical trough
I am trying to understand an interesting effect I observed while playing with my kids' toys (video). The energy in this system seems to slosh back and forth between the trough and the ball, with the ...
- 211
0
votes
0
answers
44
views
Derivation of the Lagrange equations of motion from d'Alembert's Principle specifically for rigid bodies
All of the proofs of the Lagrange equations of motion from d'Alembert's Principle I've seen so far deal exclusively with the force-inertial force balance for particles ($F-ma=0$). Despite this, the ...
- 165
1
vote
1
answer
49
views
How to prove law of mass conservation? [closed]
In our mechanics class, we began to discuss rigid movement. Let me begin with our definitions.
Definition 1: A map $f: D \subset \mathbb{E}^3 \to \mathbb{E}^3$ is rigid, if it preserves distance ...
- 179
1
vote
1
answer
30
views
Estimating angular velocity of rigid body via position
Suppose you have current state of a rigid body is $S_t = [\theta_t, \phi_t, \psi_t]$ and your past state is $S_{t-1} = [\theta_{t-1}, \phi_{t-1}, \psi_{t-1}]$
How would you estimate angular velocity ...
- 834
1
vote
2
answers
34
views
Confusion regarding kinetic energy of a rigid body
A rigid body revolves around some origin with angular speed $\Omega$. Then its kinetic energy is (parallel-axis theorem)
$$K = \frac{1}{2}I\Omega^2 = \frac{1}{2}md^2\Omega^2 + \frac{1}{2}I_\text{cm}\...
- 104
1
vote
0
answers
33
views
Proof of principle of transmissibility of force
The principle of transmissibility states
The point of application of a force to a rigid body can be moved anywhere along its line of action without changing the external reaction forces.
My question ...
- 11
0
votes
1
answer
31
views
On the identity $\vec\tau_{net}=\overleftrightarrow I_{C} \vec \alpha + \vec \omega \times (\overleftrightarrow I_{C} \vec \omega)$
Part 1
I recently came across the following identity
$$\vec\tau_{net}=\overleftrightarrow I_{C}\vec \alpha + \vec \omega \times (\overleftrightarrow I_{C} \vec \omega)$$
which gives the $\vec\tau_{net}...
1
vote
2
answers
77
views
An attempted proof of $\vec\tau_{net}=I\vec\alpha$
The statement
I attempted to prove the following statement:
$$\vec\tau_{net}=I\vec\alpha$$
for a rigid body which is only rotating about its axis and where our reference is a point on the axis of ...
1
vote
0
answers
27
views
Acceleration of Centre of Mass immediately after the application of Force
I read it in my physics textbook about the application of Force on Rigid Bodies and there I came across this case:-
So now here when force is applied to this rod which is fixed at an end [represented ...
- 23
1
vote
0
answers
21
views
FLUIDS AND RIGID BODY DYNAMICS [closed]
the question says that a door of 1*1 is hinged at its mid point and fluid is filled on its left side what force must be applied such that the gate is held stationary.
IN this my solution is attached ...
- 11
2
votes
2
answers
47
views
The motion of a rigid body [closed]
Consider a rigid body with $n$ forces acting on it. What I intend to know is how to determine the motion of the body, more specifically:
How to determine a point through which the axis of rotation of ...
1
vote
0
answers
40
views
How to derive the free rigid body equations from Euler-Lagrange? [closed]
I'm trying to retrieve the equations of motion for a free rigid body:
$$
I(t)\dot{\omega}(t)+\omega(t)^T \times (I(t)w(t)) = 0
$$
where $$ I(t)=R(t)I_{0}R(t)^T $$
I know that Euler-Lagrange equations ...
- 11
0
votes
1
answer
34
views
Clarification on force applied off COM
I was reviewing some dynamics for rigid bodies and system of particles.
In this link the author writes that the change in velocity of the COM is independent of where a force is applied to a system of ...
- 834
1
vote
3
answers
86
views
Dynamics equations for unbalanced wheel rolling without slipping on flat surface
I would like to develop a system of differential equations describing dynamics of an unbalanced wheel rolling without slipping on a flat surface. The difficulty i'm running into is that there is no ...
- 211
1
vote
3
answers
101
views
Why is Newton's second law seemingly not applicable to a ball rolling down incline plane?
A homework problem asked us to find the acceleration of a ball (pure) rolling down an incline plane without friction. I thought it was simply $a=g \ \sin(\alpha)$ where $a$ is the acceleration of the ...
0
votes
0
answers
34
views
Calculation of Accelerometer offset for Placement of Inertial measurement unit away from centre of mass
I am working on a 6DOF IMU that contains a 3-axis accelerometer and a 3-axis gyroscope, I am building a project to
plot the position and orientation of a vehicle/dirt bike in a 3d plane, However the ...
- 19
0
votes
0
answers
23
views
Self-Balancing Electric Unicycle - rider lean required for acceleration | deceleration - torque effects
A self-balancing electric unicycle consists of a frame+pedals that the rider stands on, a motor where the stator is attached to the frame+pedals, and a rotor which is attached to the wheel+tire.
An ...
- 531
1
vote
2
answers
78
views
Inertia tensor of a rigid body rotating about an axis in body-frame vs space-fixed frame
Consider a rigid body rotating about a fixed axis $\vec{OQ}=|\vec{OQ}|\hat{n}$ passing through two points $O$ and $Q$ in the body with a uniform angular velocity $\vec{\omega}=\omega\hat{n}$. With O ...
- 10.4k
2
votes
2
answers
131
views
Simulating rigid body collisions in 3d
I have been reading about physics engines and I am confused on how one approaches simulating collision responses.
I read about the coefficient of restitution:
https://en.wikipedia.org/wiki/...
- 834
0
votes
0
answers
24
views
How does the inertia tensor change when a rigid body is mirrored/flipped?
Suppose I have a rigid body $A$ whose center-of-mass is located at $\vec{u}=(u_x,u_y,u_z)$. Furthermore, let its principal axes of inertia be $\{\vec{a},\vec{b},\vec{c}\}$ and $I$ be its inertia ...
- 1
0
votes
1
answer
30
views
How to update the state of a rigid body after an impulse is applied?
When evolving rigid bodies using forces you integrate the force applied along the COM and integrating the torque using eulers equations of motion.
I am confused on how you approach this problem using ...
- 834
1
vote
0
answers
26
views
About the coincidence of angular momentum and angular velocity
Let me quote part of the answer by @knzhou , posted here
"In very basic introductory physics courses, you will usually only consider rigid bodies with an axis of symmetry, rotating about that ...
- 10.4k
0
votes
1
answer
37
views
Do rigid bodies experience work greater than or equal to that of point particles?
Consider the following two scenarios in outer space:
A yo-yo whose string is pulled by a constant force.
The same yo-yo as before although this time, the string is fully unwound and attached to the ...
- 104
-1
votes
2
answers
33
views
Kinetic energy of a rectangle rotating about its base [closed]
Take a uniform rectangle with base $b$ and height $h$ and let it rotate about $b$. The kinetic energy is:
$$ T = \dfrac{1}{2} I_b \omega^2 = \dfrac{1}{2} \dfrac{bh^3}{3} \omega^2 $$ (with $I_b$ being ...
- 91
0
votes
1
answer
64
views
What is the radius in newtons second law of motion? [closed]
We have a rod in a vertical plane rotating about a smooth fixed hinge.
After we apply Newton's second law we can say that:
$$R_n-mg\cos\theta=ma_t$$
where $R_n$ is the normal reaction due to the hinge ...
1
vote
1
answer
128
views
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 ...
0
votes
2
answers
32
views
Can the angular velocity of a prolate spheroid change over time in the absence of external forces?
Given a prolate spheroid (ie a Rugby Ball/American Football), with an initial angular velocity about an axis that coincides with one of the shape's primary axes, it seems obvious that in the absence ...
- 153
0
votes
1
answer
33
views
Rigid body motion in Arnold's book
During the study of the motion of a rigid body, in Arnold's book, two coordinates systems are introduced: one is fixed $k=\{O',\hat e_1',\hat e_2',\hat e_3'\}$ and one is inside the rigid body $K=\{O,\...
- 167
2
votes
2
answers
91
views
What would it feel as a human being to experience the Dzhanibekov Flip?
The Tennis Racket theorem describes the following effect: rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate ...
- 631
6
votes
1
answer
336
views
Is there a "most unstable rigid body shape" when spun about its intermediate axis?
Is there a shape of a solid, that provides the quickest and most violent deviation of its axis of rotation, when spun around its intermediate axis? What would be this shape and does it depend on a ...
- 171