What is Rigid body: Definition and 356 Discussions

In physics, a rigid body (also known as a rigid object ) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass.
In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electrons and nuclei) are often seen as rigid bodies (see classification of molecules as rigid rotors).

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  1. andyrk

    Characteristics of a rigid body.

    Why is the angular velocity and angular acceleration(if the rigid body has some) same for all points on a rigid body?
  2. B

    What is the Maximum Load W1 That a Supported Beam Can Hold?

    Homework Statement As shown, a uniform beam of length l = 5.90 and 48.2 lb is attached to a wall with a pin at point B. A cable attached at point A supports the beam. The beam supports a distributed weight = 21.0 lb/ft. If the support cable can sustain a maximum tension of 300 lb , what is...
  3. R

    Euler Angles/ Rigid Body application

    I apologize upfront, as I have no experience with math to begin with. However, I have a real life problem I am trying to figure out here at work and I would appreciate some help. Here is my situation: Homework Statement In a 3 dimensional plane, I have an artillery piece pointing at...
  4. T

    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...
  5. J

    Modeling Rigid Body - Unsure about Euler angles and angular velocity

    I'm modeling a single 3D rigid body in preparation for some more complicated modeling in order to gain a better understanding of Euler angles, the angular velocity vector and the rotating coordinate system. The body is rotated in inertial frame by an intrinsic ZXZ rotation, with respective...
  6. sa1988

    Rigid body, circular motion - centripetal acceleration

    Hi all, new user here and straight in with a question to help me understand something. Not sure if I'm in the right sub-forum but oh well. Regarding circular motion and centripetal acceleration, we're given the classic example of a cyclist leaning into a corner to create a general equilibrium...
  7. Y

    Torque and Angular Acceleration for a Rigid Body Problem

    Homework Statement A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 2.00kg and diameter 0.500m. After the system is released, find...
  8. H

    What is the axis of rotation for a freely moving rigid body after a collision?

    hi. I have an essential question. Suppose we have an complex shape at complete rest freely in space. There exist no forces at all. If we collide it in a point, at which axis it will be rotate? How I find it? I want the answer be in general and for all shapes.
  9. C

    Statics: Rigid Body Equilibrium

    Hello, I was wondering if someone could explain part of the solution to this problem for me. http://img706.imageshack.us/img706/5517/disksproblem.png To the right is the Free Body Diagram of Disk E, and I can draw the forces on there well enough. But I really do not understand how they...
  10. S

    What is the definition of a rigid body according to Wolfram Scienceworld?

    I would like to a complete details on rigid body motion.
  11. C

    Why is rigid body rotational energy not exactly applicable to fluids?

    I was thinking about the rotational kinetic energy of fluids the other day and I realized that I have a huge gap in my knowledge of physics. Why doesn't rigid body rotational kinetic energy (KE = 1/2*I*ω^2) not apply to fluids or deformable bodies (it should at least be proportional to that...
  12. N

    How can I calculate the depth of bullet penetration in different materials?

    Hey guys; I am new to the forums. I am an effects artist who's working a Rigid Body Dynamics project and I may be able to use some of you guys' expertise while I'm building these simulations. As I stated above, I'm doing R&D for a deformation system I'm working on. What I want to do is...
  13. G

    Using two positions on a rigid body to calculate rotation

    Hello all, I'm currently a undergrad university student doing research and I'm anaylising some position data. The data is a time-series' of Eastings (x) and Northings (y) for two points (P1, P2) on a rigid body in motion (T, E1, N1, E2, N2), with a position reported every 1 minute. I know...
  14. H

    "Statics of Rigid Bodies: 2 Questions

    2 Questions about statics of rigid bodies Homework Statement A cable of length 8.5 m is attached to the two posts as shown in Fig. 6. The crate has a mass of 1000 kg. Find the x and y components of the forces exerted by the cable on the eyebolts and find the tension force in the cable. The...
  15. Z

    Rotation of Rigid Body: Analyzing Classical Mechanics

    In the framework of Classical Mechanics,there is no problem in the rotation of rigid body.But I want to make the concept about rotation more clear. About rigid body ,there is no vibration;it would only rotate and translate.We can easily distinguish translation from rotation in rigid...
  16. Hardik Batra

    Can a body be both solid and rigid?

    What is the main difference between Solid body and Rigid body ? Can you give me example some of them !
  17. C

    Help with writing the equation of motion for a rigid body assemblage

    Homework Statement Problem figure The rigid body assemblage shown in the figure above, has a force P(t) acting upon it (varying with time). Pick a generalized coordinate such that a single degree of freedom equation of motion can be written. There is a black, massless, rigid bar. Call this...
  18. X

    Understanding 3D Rigid Body Dynamics Equations: R=R'Ω Explained

    Homework Statement I just saw the equation R=R'Ω (where ' is dot, or the derivative) in my notes (unorganized obviously), and can't remember what it stands for (rotation matrices?). Can somebody please tell me what this equations means thanks. I know R is some position vector and Ω is the...
  19. L

    Force on rigid body: translation or rotational acceleration?

    Homework Statement A perpendicular force F acts on the tip of a thin rod of length L and mass M in the ij-plane which is not fixed. What is the translational and rotational acceleration of the rod about the center of the rod? Homework Equations At first it seems like an easy problem...
  20. M

    Conservation of Energy in a Rigid Body

    Homework Statement I'm having some trouble understanding "conceptually" the following problem (example 6.18 in Kleppner and Kolenkow.) A stick, initially upright, starts falling: find the speed of the center of mass as a function of position. Homework Equations Work-KE thm. for a rigid...
  21. J

    Equilibrium of a Rigid Body

    Homework Statement Suppose the ruler in procedure 3 is asymmetrical, balancing at the 60.2 cm mark. The ruler is now supported at the 41.3 cm mark, and a mass of 364 g is placed at the 26.2 cm mark. Find the mass of the ruler. The ruler is 1.00 m long. Homework Equations...
  22. T

    Rotation of a Rigid Body: Finding Center of Mass and Moment of Inertia

    Homework Statement A 0.9 kg mass at (x, y) = (20 cm,20 cm) and a 2.0 kg mass at (20 cm,100 cm) are connected by a massless, rigid rod. They rotate about the center of mass. Homework Equations x=(m1*x1+m2*x2)/(m1+m2) y=(m1*y1+m2*y2)/(m1+m2) I=1/12*ML^(2) The Attempt at a...
  23. B

    Stuck on derivation of Euler's equations in rigid body dynamics

    i was reading about derivation of Euler's equations for rotational dynamics (john taylor, classical mechanics, chapter 10) when i got stuck on one of the reasonings essentially it refers to the moment of inertia tensor, since the tensor itself about a point is dependent on the position of the...
  24. C

    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...
  25. M

    What do you mean by rigid body?Can anyone tell me why rigid body does not exist?

    Hello, Does anyone knows why rigid body does not exist.So in order to know its history which textbook can i refer to ? For example to know classical mechanics properly you have to go to Newtons book known as Principia. In order to know rigid bodies who should we refer.
  26. A

    2D equilibrium of a rigid body

    Homework Statement http://i.imgur.com/0h6dF.png Homework Equations ƩFx=0 ƩFy=0 ƩMo=0 The Attempt at a Solution not sure what unknowns are
  27. A

    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. N

    Angular Momentum Projection of a Rigid Body: Formula & Proof

    Hi everyone! Which is the formula and the proof of the projection of the angular momentum of a rigid body along the rotation axis? I searched on the web and on my mechanics book but cannot find anything... does somebody know this curiosity ?
  29. L

    Formulation rigid body constraint

    Hello I need some help with formulating the constraint force for a sliding and rotating box. The scenario is: A box is sliding down a slanted table. The center of gravity has passed the edge of the table so the box receives a counter force and torque. I am solving the forces and moments...
  30. M

    3D Rotation of a rigid body in Fixed Axes (Not Axes Rotation)

    Dear All, I have come across with a seemingly very simple problem but could not solve it by searching on internet and books. May be I am confused. I want to rotate a 3D body around an arbitrary axis with fixed principal axes. The solutions I found is with Euler angles (Euler rotational...
  31. Q

    3D Rigid body dynamics - Rod over rotating disk

    Homework Statement A thin uniform rod is attached to an axis through its midpoint. The axis is standing on a disk rotating with constant angular speed \Omega about its symmetry axis. The rod's midpoint is located directly above the rotational axis of the disk. Let \theta denote the rod's...
  32. B

    Rigid Body Motion: Determing Angular Momentum Equations

    Hello, I'm trying to determine whether my work for the following rigid body motion is correct, and if so why I'm not able to verify equivalent formulations. For the sake of simplicity small angle approximations will be used, and cross terms were neglected. Homework Statement...
  33. J

    Support force vectors for a fixed rigid body

    Hello all! I'm a programmer looking to put together a system modeling the force a character's limbs exert on the environment as that character moves around. Characters can either grasp (with a hand) or press against (with a foot or something) viable contact points in the environment in order...
  34. S

    AI optimal rotation of a rigid body

    I'm trying to write AI code for a program, in which a spaceship has to rotate to face a target. I've somewhat idealised the situation - the ship can yaw, pitch and roll with a maximum angular acceleration along each axis. I'm representing the rotation of the ship relative to the world...
  35. A

    Rigid body kinematics problem: finding the velocity of the center of mass

    I have to deal with the problem of finding an expression for the kinetic energy of a rigid body. One of its point is pivoted to a point that moves arbitrarily. So in order to find an expression for the kinetic energy I use König's theorem, but I need the velocity of the center of mass. I use...
  36. B

    Rigid Body on Frictionless Surface

    Hey all, Say you have a slab sitting vertically(like a door) at rest on a frictionless surface. If you push with a horizontal force somewhere near the top(as long as it is above the center of mass), would the slab rotate(tip over)? My friend and I were originally thinking of how much...
  37. D

    Contact Point between a Rigid Body and the Surface it sits (Semi-Ellipsoid)

    Hello, I've been having trouble with a certain part of a homework problem. I wish I had posted this earlier so there would be more time! Anyway... The shape is a semi-ellipsoid (a Rattleback, in particular). Here's a good picture of what I'm talking...
  38. A

    Rigid body (rectangular) collision with wall

    Hello, I have a rectangular object with the following properties: Mass (m) = 1 units Moment Of Inertia (I) = 4.41 units initial velocity (v_{i}) = (5, 0) initial angular velocity (w_{i}) = 0 If the block collides with a solid rigid wall with distance vector r = (1.1, 1.4) from the...
  39. B

    Rigid Body- Derivation of Momentum Equations

    Homework Statement Hello, I'm having some issues deriving the momentum equation for rigid body motion in a non-inertial frame. Consider a rigid body moving in a two dimensional (inertial XY) plane. A body fixed frame (origin denoted as B) is located off the center of gravity. The body has...
  40. C

    Model a rigid body made of two points linked by a rigid bar

    Hi all! I need help..:) I need to model the dynamic of this system: I'm in the plane (2-dimensions). There are two points (with m1 and m2 masses) free to move with different speed vectors (in module and direction). At some point, when the distance between them is d, the two points...
  41. B

    How to Calculate Torque of a Leaning Rigid Body

    So this is a conceptual question, it's not a direct homework question, but it does involve how to do a kind of calculation. I hope this isn't the wrong place to post a nonspecific question like this. In the case of a board/stick/ladder leaning against a wall, about an axis O at the bottom of the...
  42. G

    Equation of motion for a rigid body

    hi let me says you have an arbitrary rigid body and a force F acts on this body at some point A, which is not the center of mass that is called C. how do you get the equation of motion? my idea was to separate out translation and rotation: maybe the whole body moves by F=ma and...
  43. A

    Solve Rigid Body Collision: System Approach w/Cons. Angular Momentum

    under what conditions can a rigid body collision problem be solved using a system approach, (i.e by using the conservation of angular momentum of the two rigid bodies about some point) the equation M=d[H]/dt is only valid when M and H are taken about a point fixed in a massless extension of a...
  44. A

    Rigid Body Dynamics: Rising the Rough Rod

    A perfectly rough rod is gently placed with one end upon another rod of equal mass and in the same vertical plane, moving with the velocity √2gc on a smooth table. If the initial inclination of the first rod to the horizon be α, and its length 2a, shew that it will just rise to a vertical...
  45. Femme_physics

    Do the solutions have an error linear+rotational motion of a rigid body

    I find it hard to believe I forgot my mechanics... I think the solution manual has a mistake Homework Statement http://img225.imageshack.us/img225/8018/mech1l.jpg Homework Equations http://img337.imageshack.us/img337/8733/mechform.jpg The Attempt at a Solution...
  46. X

    Rigid body dynamics (kinematics of a point)

    Homework Statement See attachment "problem" Homework Equations The Attempt at a Solution See attachment "work" and "answer" I got 0.92, but the book gives 1.73. Something went wrong, but I can't find it.
  47. E

    Calculating 3D Impact Coordinates for Golf Ball Collisions

    hi there, I have been working on this particular problem for some weeks?months? now, and it has me quite stumped. I need to calculate the x,y,z co-ords of a golf ball after it has been putted into a hole, when it contacts the opposite rim, assuming it is traveling fast enough to contact the...
  48. N

    Center of mass for rigid body and point particle

    Hi, this is a problem on center mass. Homework Statement A beam hangs straight down from a point O(O is placed at x=0 and y = 0, aka origo). The beam is attached to the point O. Beam has length L and mass M. The density of the beam is uniform, so the centermass of the beam is...
  49. A

    Rigid Body Dynamics - 4th Equation

    Let's say there are two rigid bodies in space, each has an initial translational velocity as well as an initial angular velocity. Eventually, these two bodies collide. The collision causes the translational and angular velocities of both bodies to change, resulting in 4 unknowns (each unknown...
  50. B

    Rigid body angular velocity limit

    Suppose a rigid body (say a sphere) ofis rotating with angular velocity A. Any point at a distance r from the axis of rotation has tangential velocity v=A*r and that v must be less than c. Does this mean that : 1. The rigid body can only be a certain maximum (radial) size r, where r<A/c? 2...
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