# What is Rigid body rotation: Definition and 33 Discussions

In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior.
The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law (kinetics) or their derivative form, Lagrangian mechanics. The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.

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1. ### Angular momentum of rotating hoop

Problem: Official solution: My calculation: \begin{align*} \mathbf L &= M \mathbf R \times \mathbf V + \mathbf L_{cm} \\ &= M R (\hat j + \hat k) \times (- \Omega R \hat i) + MR^2 \Omega \hat j \\ &= MR^2 \Omega (\hat k - \hat j + \hat j) \\ &= MR^2 \Omega \hat k \end{align*}
2. ### Understanding Kinetic Energy: Moment of Inertia and Rotational Motion

Consider the above setup. Here, to get the kinetic energy of the body, the moment of inertia with respect to the ##y-##axis has to be calculated. This can be done in two ways: 1. The moment of inertia of the rotation around the center of mass is ##\Theta_s##, then the kinetic energy is...
3. ### I Intuition Behind Intermediate Axis Theorem in an Ideal Setting

For a rigid body with three principal axis with distinct moments of inertia, would the principal axis with the intermediate moment of inertia still be unstable in ideal conditions, e.g. no gravity, no friction etc.? From the mathematical derivation I deduce that it should be unstable, since we...
4. ### I Gravity on an unbalanced object

So I have 2 Points P1 and P2. P2 is the center of mass which has an X and Y coordinate. P1 is where I think that it will fall over from and only has an X location. Now what I want is to find a way to get how far the angle at P1 will change in relation to where these points are within a given...
5. ### Stability of rigid body rotation about different axes

We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy. However, for this question involving a rigid body, the most stable axis is the one with the lowest moment of inertia...
6. ### Rigid body rotation -- A person walking around a merry-go-round

This one is challenging for me. Can anyone give me a hint?
7. ### Rigid body rotation problem: Mass on a cord spinning up a wheel on an axle

(I know how to solve the problem, that's not what I am looking for.) I have a problem with how I ought to understand the moment of inertia. The only torque I see applicable on the wheel is that of the tension, and so I think that ##I## should be ##m_{\text{point}}R^2##, without including all the...
8. ### Euler Equations for Dynamics of rigid body

I have been studying the dynamics of free top from Morin's book. In his book when describing the dynamics,he writes down the equation of motion as shown in screenshot. However,I am not able to understand which term refers to which coordinate system. For eg: Here ##\omega## refers to angular...
9. ### Rigid Body Rotation relative velocity question

This is a question about the concepts behind rigid body rotation when we use relative velocity. In general, let us say that we have a rigid body and on it are two points, A and B, which are moving with velocities vA and vB respectively. These velocities are in random directions. The theory...
10. ### Understanding Rigid Body Rotation: Solving Problem 4A and B from a Physics Exam

I am trying to solve problem number 4 part A and B from (http://people.physics.tamu.edu/kamon/teaching/phys218/exam/2003C/2003C_Exam3_Solution.pdf) but I am confused about certain aspects of it. In part A, I understand that since we are considering the person as a cylinder, the equation for...
11. T

### Understanding Rigid Body Rotation: Principles and Observations

Just to confirm a few points: A body frame rotates with a body. It need not be aligned to the rotation axis. Angular momentum vector always aligned with rotation axis (not deviates from it). An observer on the body surface (body frame) observes no motion on a body. Principal axis of rotation...
12. ### A How can I find the collision time of 2 ellipsoids that rotate

I have 2 ellipsoids: Ax^2/a^2+Ay^2/b^2+Az^2/c^2=1; (*a,b,c>0 constants*) Bx^2/a^2+By^2/b^2+Bz^2/c^2=1; Ellipsoid A rotates around axis [wax;way;waz] (unit vector) with an infinite speed; Ellipsoid B rotates around axis [wbx;wby;wbz] (unit vector) with an infinite speed; [Dx;Dy;Dz] is the vector...
13. ### Rigid body with center of rotation other than CoM

Suppose we have a rigid body that rotates around a point P other than its center of mass, with point P being a point of the rigid body. This implies that there are external forces to the rigid body. If the external forces cease to exist(like we have an axis passing through P and we suddenly...
14. ### MHB Disc Rotation: Mass m & Radius r Down Slope of tan^-1 3/4

a disc of mass m and radius r rolls down a slope of incline tan^-1 3/4. the slope is rough enough to prevent slipping. the disc travels from rest a distance of s metres straight down the slope. (i) show that the linear acceleration of the disc is 2/5 g. what i did was i first revolved the forces...
15. ### I Can every shape precess like a top (toy)?

The main question is in the title. 1.I have wondered if a regular pencil would precess and rotate stable for multiple seconds if spun fast enough. [Coins, plates, bowls and similarly shaped objects can rotate in a stable way for extended periods of time. And a lot of other household objects...
16. ### Angular acceleration in rigid body rotation due to a torque

For the rotation of a rigid body about a fixed axis z the following holds. $$\vec{\tau_z}=\frac{d\vec{L_z}}{dt}= I_z \vec{\alpha} \tag{1}$$ Where \vec{\tau_z} is the component parallel to the axis z of a torque \vec{\tau} exerted in the body; \vec{L_z} is the component parallel to the rotation...
17. ### Component of angular momentum perpendicular to rotation axis

Homework Statement Consider the rigid body in the picture, rotating about a fixed axis z not passing through a principal axis of inertia, with an angular velocity \Omega that can vary in magnitude but not in direction. Find the angular momentum vector and its component parallel to z axis (...
18. ### Moment of thin Rod at pivot when acted upon by a Force

This is of my own interest/ practice. Homework Statement A thin rod (of width zero, but not uniform) is pivoted freely at one end about the horizontal z axis , being free to swing in the xy plane (x horizontal, y vertically down). Its mass is m and its CM is a distance a from the pivot. The...
19. ### Query on the Euler Theorem for Rigid Body Rotation

Hi, I am having some problems conceptualizing the Euler's Theorem. Any help will be greatly appreciated. In Goldstein's book the Euler's theorem is stated as 'Any displacement of a rigid body, whose one point remains fixed throughout, is a rotation about some axis', then he has proven that the...
20. ### Rotation of a rigid body about external axis

in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body - Rotation of a rigid body about a fixed axis is defined as...
21. ### Instability of free rigid body rotation about middle axis

Hi everyone, I was recently talking to someone with a non-maths background about rotational stability, in particular how rotation is stable around the largest and smallest principal moments but not the intermediate one. He asked me if there was any 'obvious' reason for this, but one didn't...
22. ### Can I apply Bernoulli's equation to rigid body rotation?

1. The problem statement, all variables and given/know Say I have a can of water, and I am rotating it about its central axis at a constant angular rate. The water in the tank should make a 3D almost parabolic curve as it touches the the walls of the tank. Can I use Bernoulli's equation along...
23. ### What happens when you rotate a rigid body

Hi, I have a question about rigid body rotation. If I have a rod out in space in free float and I attach a battery powered fan to center of mass and then the fan is turned on to spin in a clockwise direction, then the rod should spin in a counterclockwise direction. This much I...
24. ### Rigid Body Rotation: Proving/Disproving \vec{R'} Direction

Homework Statement This is not a HW problem, but something I am trying to prove/disprove for my own knowledge. I have a tube pinned at both ends and inclined in the x-y plane. The pin locations can both move freely in space but subject to the constraint that the tube will not stretch or...
25. ### Torque and rigid body rotation

Hello. My first post here. I'm having trouble with the basics of rigid body rotation. I have a few questions (my apologies if they are too childish; I'm very new to this): 1) Is torque (and other angular parameters like angular velocity, angular acceleration etc.) defined about a point or an...
26. ### Rigid body rotation near galactic center

Homework Statement Equate the expression for centripetal acceleration with the gravitational acceleration to show that the central parts of the galactic rotation curve are consistent with rigid body rotation. The attempt at a solution Say a star near the galactic center has mass m and the...
27. ### Rigid body rotation. Need explanation

Homework Statement https://dl.dropbox.com/u/66988308/Capture.JPG Homework Equations V=rWThe Attempt at a Solution I tried to plug in the forumla , and algebras but I keep getting rc/rf as answer instead of rf/rc as the book says. Work: Vf=(rf)W W=Vf/rf W=Vc/rc Vc/rc = Vf/rf (Vc)(rf) = (Vf)...
28. ### Rigid Body Rotation: Find Vel & Action on Axis in Eq. Pos.

Homework Statement A system is made of the following things: A homogeneous disk of mass m = 4kg. Having radius r = 80cm's. A point P (m = 2kg) free to rotate around a horizontal axis which is perpendicular to the disk in point A. AO = OP/2 If the system starts from rest and AP forms a...
29. ### Rigid Body Rotation Application

Homework Statement I'm trying to include rigid body rotation in a problem I'm working on but can't seem to figure it out. Two shafts oriented vertically are connected by a thin cross member of length R. Holding one shaft stationary and applying a constant tangential load F to the other...
30. ### Rigid body rotation about a moving axis

Note this is physics I This should be the right section as this is not homework.. Ok I'm having trouble understanding the concepts of rolling without friction, kinetic energy linear and kinetic energy rotational. I have a hard time following my professor in class and usually like to go...
31. ### Rigid Body Rotation: Calculating Load Supported by Pivot

Homework Statement imagine a thin length of wood supported by two supports, one at either end. One support dissapears and the other turns into a pivot (as gravity acts on the wood). Show that the load supported by the pivot is Mg/4. The Attempt at a Solution i don't know where to...
32. ### Deriving the Moment of Inertia for a Rod with a Pivot at One End

a plank is conected horizontally at both ends to two points. One of the points dissapears and the other turns into a pivot. show that the Planck of length l,mass m pivoted at one end has an acceleration (3/2)*g initially i used parallel axis theorm do derive the moment of inertia of a...
33. ### Can Fluid Dynamics Explain Non-Vertical Gravity Fields in Fast Rotating Bodies?

I have found many cases of fluids entering rigid body motion where the gravity vector is purely down the rotation vector. I am curious if there is a soultion for where the gravity vector is in another direction. I've attempted to solve this myself for a particular rotation, but it is so fast...