Rigid body Definition and 356 Threads

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. U

    Total derivative involving rigid body motion of a surface

    This stems from considering rigid body transformations, but is a general question about total derivatives. Something is probably missing in my understanding here. I had posted this to math.stackexchange, but did not receive any answers and someone suggested this forum might be more suitable. A...
  2. B

    Rotation of fluid like a rigid body in a cylindrical contain

    Hello! While studying from the book 'Fluid Mechanics' by Cengel I came across the section which explains the behavior of fluids acting like a rigid body when the cylindrical container which contains the liquid rotates with a uniform angular velocity. Without much explanation the author states...
  3. S

    Kinetics of a rigid body (conservation of energy)

    Homework Statement [/B]Homework Equations [/B] (1) (pink) Is it vertical displacement ? * 4 - 2 (unstretched length of the spring) ? (2) (blue) What does it mean ? * I was thinking that maybe they used The Pythagorean theorem (62+42)=7,2 ≅ 7) but I'm not sure. Besides I don't understand...
  4. almarpa

    Euler equations in rigid body: Taylor VS Kleppner - Kolenkow

    Hello all. After reading both chapters on rigid body motion both in Kleppner - Kolenkow and Taylor books, I still do not undertand the physical meaning of Euler equations. Let me explain: In Kleppner - Kolenkow, they claim (page 321 - 322) that in Euler equations, Γ1, Γ2 and Γ3 are the...
  5. ognik

    Angular momentum of rigid body elements tensor

    Homework Statement I was working through my text on deriving the tensor for Angular momentum of the sums of elements of a rigid body, I follow it all except for one step. Here is a great page which shows the derivation nicely - http://www.kwon3d.com/theory/moi/iten.html I follow clearly to the...
  6. N

    Rigid body physics simulation math issue

    Hey all, I'm making a physics simulation for training an algorithm of mine, I'm running into issues on the rigid body physics simulation. Let's say I have a leg composed of a calf and a thigh. gravity will be acting on both, and the calf is attached to the thigh, Any suggestions on how I would...
  7. P

    Calculating Kinetic Energy of a Rotating Grinding Wheel

    1. A grinding wheel of mass 5 kg and diameter 0.20 m is rotating with an angular speed of 100 rad/s. Calculate its kinetic energy. Through what distance would it have to be dropped in free fall to acquire this kinetic energy? m = 5 kg, r = 0.20/2 m = 0.10 m, g = 10 m/s2, ω = 100 rad/s 2. v =...
  8. Feodalherren

    Rigid body dynamics: falling stick

    Homework Statement A stick of length L and mass m is falling on a table with kinetic friction uK and static friction uS. Find the equation that determines whether the rod will stick or slip. If m = 10kg and L = 100cm, uS = 0.8, uK = 0.7 and initial theta = 30 degrees find the initial accel for...
  9. hdp12

    Internal Force Diagram for Rigid Body and Distributed Load

    I'm working on a homework problem for Statics and I'm stuck. Could someone please help?Problem: Draw the internal force (N,V,M) diagrams and include all significant figures Here is all of my work: Resulting F from W1: W(x) = W1 ∴ F2=∫02b W1dx eq (1) ⇒ F2 = W1⋅2b x1 = (F1)-1 ∫02b W1dx =...
  10. stipan_relix

    A homework assignment including rotation of a rigid body

    Homework Statement The problem is this: A car is evenly slowing down from 30 km/h to 0 in the time of 2 seconds. Radius of its wheels is 30 cm. What is its angular acceleration and what total angle will the wheel describe until it stops? How many turns does the wheel make and what is the length...
  11. A

    Direction of instantaneous axis in rigid body dynamics

    The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded...
  12. J

    Solid hemisphere resting on an inclined plane

    Homework Statement A solid uniform hemisphere rests in equilibrium with its curved surface in contact with a rough inclined plane which is elavated by an angle α where sin(α) = 3/16. Find the angle between the symmetry axis of the hemisphere and the vertical.[/B]Homework Equations Sine rule...
  13. hdp12

    Given Moment about a Pin and a Roller

    Homework Statement For my statics homework, we are directed to: Draw the free body diagram and use the force and moment equilibrium to determine the support reactions for the following systems I'm having a bunch of trouble with problem 4.10, which is displayed in the following picture I'm...
  14. T

    Finding angle required for equilibrium on a slope

    Homework Statement A heavy uniform cylindrical drum is placed, with its axis horizontal, on a slope inclined at an angle α to the horizontal. It is prevented from sliding or rolling down the slope by a triangular wedge. The weight of the wedge is negligible compared with the weight of the drum...
  15. A

    Engineering Instantaneous Center of Zero Acceleration of Rigid Body

    hi i am araz a mechanic master engineer and i am looking for any article or information about" Instantaneous Center of Zero Acceleration of Rigid Body" because i couldn't find any but "Instantaneous Center of Zero velocity":confused: i hope here i can find some help?!
  16. M

    Component of angular velocity in rigid body motion -- which is right?

    Let w = (w1, w2, w3) wrt to the body frame of a rigid body, where the body frame is right-handed orthonormal. I have gathered 2 definitions of w from different sources and I am confused at how they connect to one another. One is that the RB rotates about w through its CoM at rate abs(w), the...
  17. B

    Rigid Body Motion/Out of convergence in ansys Classic 14.5

    Hi all, I am analysing a 2D D-shaped Neo Hookean model in contact with a Rigid link. The details are in the input file attached. Can someone guide me on how to solve this issue?:headbang: Thanks, Bruce
  18. AdityaDev

    Is the expression still valid for large differences in radius?

    If a ball rolls in a semicircular track starting from one end of track,( the track is kept vertical) and if radius of ball is r and radius of track is R is this expression correct? (When ball reaches lowest point) ##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2## where...
  19. A

    Vibration of Rigid Body with One Spring: Understanding Torque Equations

    Homework Statement Rigid body with one spring. Homework Equations Torque equations ( M=I * "alpha") The Attempt at a Solution So I think I can solve this problem but there is only one thing I do not understand. When I am writing my torque equation I would think that the weight of the bar...
  20. Glomerular

    Lagrangian - rigid body problem

    Homework Statement In a uniform gravitational field, there is a uniform solid disk of of mass M and radius R. A point mass m is glued to the disk at a point that is at a distance a from the center of the disk. The disk rolls without slipping. Find the frequency of small oscillations about the...
  21. J

    Rigid Body Collision: Angular Velocity Question

    So I'm upgrading my Physics Engine's Collision response system (don't worry, this is a pure physics question, no programming involved! Also don't worry about the time of collision, my collision detection system is separate and returns a time of collision for the response system to work with) and...
  22. Q

    I have a question about a problem of conservation of momentu

    Momentum in rigid bodies; In this problem when I draw all the forces acting on the disc A, would the reactions: Ax, Ay; W, Friction, normal force; I do not understand is how to check that Ay = W, that's what I understand from the solution. Anyone have any tips on how to treat reactions in such...
  23. T

    Rigid Body Rotational or Translational ?

    In the figure A has mass 4 kg. B and C are identical uniform discs, each of mass 2 kg. The string supporting A is ideal. Obtain the acceleration of A I have just one question, Why is pulley C undergoing translational motion ?, it should be rotational motion because it rotates about a fixed axis
  24. T

    FBD of Flexible and Rigid Body Coupling

    Problem: I am having a bit of problem with the signs on the force balance with the constraining force. The system is: Attempt: I drew the FBD with the constraining force for the lumped mass: Then I tried to solve for the constraint force in terms of the spring and damper: For the...
  25. AdityaDev

    Conserving Angular Momentum (Rigid Body Dynamics)

    Lets say i have a rod (length = L) hinged at one end (A).It is initially at rest.Now if an impulse (J) acts on the other end (B),can i conserve the angular momentum about A(the hinge)? that is can i write: JL=Iw?(I=moment of inertia,w=angular velocity) this is what i saw in the book. My Doubt...
  26. Lord Crc

    Rigid body, torque and moment of inertia

    Hi, it's been quite some years since I took some entry-level mechanics at uni, and my book is no longer with me, so I'm struggling a bit here. I'm making a very simple rigid body simulator just for fun, but the angular velocity is not working out right. I suspect I've forgotten something...
  27. D

    Conservation of Momentum and Kinetic Energy in Collisions with Rigid Bodies

    I'm having trouble with this line from Goldstein-"the center of mass moves as if the total external force were acting on the entire mass of the system concentrated at the center of mass." If a bar is floating in space (at rest in the frame) and a point mass strikes the bar perpendicular to...
  28. Delta2

    Dual role of force acting on rigid body

    Can the same force increase both the translational and rotational kinetic energy of a rigid body? If yes then the work done by the force equals the sum of the increase in the translational and rotational kinetic energy?
  29. L

    Work done on a rigid body in a collision

    Sorry if this question has already been considered in this Forum (I'm sure it is but I can't find it now). A rigid ball slide without friction in an horizontal plane and collide elastically with a wall, the plane of which is perpendicular to the ball's velocity. During the collision the ball...
  30. K

    What are the Equilibrium Conditions for a 3D Rigid Body with Applied Forces?

    Homework Statement The rod assembly shown has a ball-and-socket joint at A and a smooth journal bearing at C. The forces F1=600N , F2=410N , F3=460N , and F4=950N are applied as shown in the figure. The geometry of the rod assembly is given as a=0.900m , b=0.650m , and c=0.800m...
  31. S

    Classical mechanics - rigid body rotating

    Homework Statement Around vertical axis ##O## a body on picture below (see attachment) is being rotated with constant angular velocity ##\Omega ##. On the circle we have a body with mass ##m##, that can feels no friction. Find position of that body as function of ##\phi ## and time. Calculate...
  32. Saladsamurai

    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...
  33. L

    EoM for rigid body, wrench and twist help

    I am currently working on a robotic manipulation problem and need to form a model for how an object responds. I start by writing up the equations of motion for the body, the motion is then constrained by an additional constraint equation. However, I am new to the notions of twists and wrenches...
  34. N

    Mechanics behind laminar motion of rigid body

    A ridig sphere is rolling from left to right down an incline plane with an angle elevation of β In the y -direction, FN = mg cos β. In the x-direction, mg sin β - f (where f is the frictional force: μsFN) The laminar motion is then given by Icmdω/dt = Rf (where R is the radius of the sphere)...
  35. E

    Doubt in equilibrium of rigid body

    Hello there! I am currently studying the equilibrium of rigid body and encountering a doubt. Now, in their explanation of reaction forces by a roller or a rocker or a smooth surface, they generalize it as in the preceding examples prevent the translation of a beam for example in ONE direction...
  36. M

    Equilibrium of a Rigid Body: Finding Unknown Mass on a Lever

    Homework Statement Find the unknown mass on a lever (see-saw). I have three masses. To the right of the fulcrum, the mass is 166 g and it is 25.15 cm from the fulcrum. There are two masses to the left. One is 166 g and is 16.95 cm from the fulcrum. The unknown mass is 3.33 cm from the fulcrum...
  37. A

    Combined translational and rotational motion of a rigid body

    The velocity of any point P of a rigid body in rotation plus translation is \vec{}vp=\vec{}vCOM+\vec{}vp,COM. Now |\vec{}vCOM|=v and \vec{}vp,COM =rω . But v and rω are same thing as v=rω ,so velocity of the particle every time will be √2 v.Then what is the difference between \vec{}vCOM and...
  38. C

    Angular and linear velocity of a rigid body given a force.

    Hello, I'm trying to prove a simulation of mine is working correctly. the simulation has a cube of sides 1, mass 1 and c.o.m. position at (0,0,0.5) ie sitting on the xy plane. i have a force along the x-axis of 10. Is there anyway given those two, that i can work out the resulting ω and v of...
  39. A

    Angular velocity of rigid body

    Dear All, i was reading a book in which it is written that if a rigid body have both rotational(with angular velocity 'w' about its center of mass)and translation(with velocity 'v' of center of mass) motion then the whole motion can be treated as an equivalent motion of pure rotation about...
  40. M

    2D Rigid Body Dynamics - Newtonian Equaitons of Motion

    Homework Statement In the diagram attached a bar weighs 500 kg and is a 2D plane rigid body with mass centre at G. At the instant shown, the bar is moving horizontally at but reducing speed, causing horizontal deceleration as shown by vector a=-7i m/s2. At the same time, the bar is being...
  41. R

    Statics Rigid Body Equilibrium Problem

    Homework Statement The given force F is equal to 5000N,γ=〖30〗^o and α=〖15〗^o. The moment on member 4 is to be found. The geometry of the structure was worked out separately. Homework Equations To solve the problem I tried to use the Equilibrium equations which state that...
  42. K

    Does rotation of rigid body need a couple or only 1 force is sufficien

    Hi all, Suppose we go in space where no gravity and friction exists. If there is a bar, in say - horizontal plane and we apply a force at one end of the bar, in this plane and perpendicular to the bar. Will that bar rotate and translate or it will only undergo pure translational motion...
  43. U

    Angular acceleration, rigid body

    Homework Statement A circular disk with the mass m and radius r is hanging from two ropes with length l when suddenly the rope ED snaps. For this moment, find: a, The angular acceleration for the rope OB, the angular acceleration for the disk b, The force T acting in OB The Attempt at...
  44. AakashPandita

    Rigid Body Rotation: Axis Points Stationary?

    In rotation motion do points through which the axis passes also rotate or are they stationary?
  45. F

    Inertia - Moments of Inertia of a rigid body (different axes)

    Inertia -- Moments of Inertia of a rigid body (different axes) Here is the problem http://imgur.com/pL6Bdgw So I missed class today because I was studying for a genetics test. I don't need the answer or anything but I was wondering what the general rule for inertia that I would use for...
  46. B

    What is axial rigid body motion?

    What is axial rigid body motion? Is it along Z-axis?
  47. L

    Rigid Body Kinetics: Find Reaction Force at A

    Homework Statement As the picture says, we are trying to find the reaction force on the bearing at A: We are given: M(block) = 26.1kg M(bar) = 8.7kg L(bar) = 1.8m V(block) = 6.2m/s Homework Equations What I have attempted the solution with are: ƩF = ma ƩM = Iα I0 = (m*L^2)/12...
  48. G

    Rigid Body Kinetics: Angular Acceleration of Rod w/ Friction Torque

    Homework Statement A long slender rod has a mass of 0.66 kg and a length of 648.0 mm. The friction torque at the hinge is 0.41 Nm. What is the angular acceleration of the rod when it is 38 degrees below the horizontal? Homework Equations The Attempt at a Solution Torque =...
  49. M

    Clarification in concept of planar motion of rigid body

    When a Rigid body is said to be in planar motion, if all all the particles in the Rigid body moves in same plane and these planes are parallel to each other. I think i misunderstood this definition especially the particles moves in same plane and these planes are parallel to each other...
  50. A

    Relative Velocity, Rigid Body Kinematics

    Homework Statement W(oa) = -5k α(oa) = 3k B = 30 deg B(dot) = -2cos 30i + 2sin30j = Vrel b(double dot) = 4cos30i - 4sin30j) Homework Equations Va = Woa x Rao + Vrel The Attempt at a Solution This is such a simple problem and I don't know why I am messing it up. I am just...
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