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. D

    Angular momentum of a rigid body

    A 0.15 meter long, 0.15 kg thin rigid rod has a small 0.22 kg mass stuck on one of its ends and a small 0.080 kg mass stuck on the other end. The rod rotates at 1.7 rad/s through its physical center without friction. What is the magnitude of the angular momentum of the system taking the center...
  2. C

    Kinetic Energy Calculation for Rigid Body Lagrangians with Two Particles

    Homework Statement two particles, m_{1}, and m_{2} are connected together by a thin masses rod of length d. The system moves under a uniform potential function U(r_{1}^{\rightarrow}, r_{2}^{\rightarrow}). What is the Kinetic energy of the system in cartesian coordinates? Homework Equations...
  3. O

    Can You Solve This 2D Equilibrium Problem with a Pirate on a Plank?

    Homework Statement The pirate is walking the plank. If the plank weighs 500 N and the weight acts at the centre of the plank, how far (distance x) can our pirate, who weighs 780 N, walk before the plank tips and he falls. All dimensions are in meters. ANS: 0.769 m (Look at picture)...
  4. S

    Rigid Body Collisions: Physics for 2D Simulations

    Hello, I am new here, so I don't know if this is the right place to post this question or not, if not please move it to the right place. At the moment I am working on making a computer simulator for rigid bodies using java, the only problem is that I thought that high school physics would...
  5. H

    What are the reactions at the base of the light pole in fig.1?

    Homework Statement Determine the reactions at the base of the light pole shown in fig.1 Homework Equations Summation of force and moment of a system in equilibrium is 0. The Attempt at a Solution The resultant force of due to the weight of the light pole and lamp is 185g N...
  6. A

    Rigid body dynamics question

    Hi! I have been working on a rigid body subject quite a long. But till now there is an unresolved question for me. When we calculating the torque acting on the rigid body we use the following definition of the torque: t = r X f, X - is a cross product. So if I calculate the torque in a...
  7. N

    Rotation of rigid body - wobbling

    When a rigid body experiences a rotation about an axis other than one of its "principal axis of rotation", it experiences a "wobble" I have been trying to understand why this is so (intuitively). Here is what I have come up with - please tell me if I have misconceptions or...
  8. S

    Rigid Body Physics: Box on Plane Simulations

    Hi, I am new to these forums so i hope I am putting this in the right place... I am completely lost with how to even start a simple box on plane physics simulation. I've read dozens of formulas and tutorials, I understand them mostly but they all seem very abstract in the sense of how to use...
  9. L

    Moment of Inertia Tensor for a Flat Rigid Body

    1. Problem I need to find the principal moments of inertia about the center of mass of a flat rigid 45 degree right triangle with uniform mass density. 2. Useful Formulae I_{xx}=\int_{V} \rho (r^{2}-x^{2}) dV I_{jk}=\int_{V} \rho (r^{2} \delta_{jk} - x_{j} x_{k}) dV 3. Attempt at a...
  10. E

    Multiple forces acting on a rigid body

    Hi, I'm attempting to do a simulation of rigid bodies dynamics, and have ran into a problem. Homework Statement It can and at some point will occur that multiple forces will be acting on a rigid body, at different points with different strength and under different angles. Obviously...
  11. S

    Rigid body motion and game physics

    I am just playing around with physics simulation in c++... and my latest obsession is simulating rigid body motion (specifically rotation) with no external torque, for now. The equations of motion in question are the 'Euler equations' which relate the angular acceleration (omega-dot) around any...
  12. L

    Equilibrium of a Rigid Body question

    The solid uniform disk of radius b shown can turn freely on an axle through its center. A hole of diameter D is drilled through the disk; its center is a distance r from the axle. The weight of the material drilled out is Fwh. Find the weight of an object hung from a string wound on the disk...
  13. E

    Calculating Moment of Inertia for a Rigid Body

    Homework Statement A rigid body consists of three thin uniform rods, each of mass m and length 2a, held mutually perpendicular at their midpoints. Show that the moment of inertia is the same for any axis passing through the origin. Homework Equations The Attempt at a Solution I...
  14. M

    Is Torque Equal on All Axes When a Rigid Body's Net Force Is Zero?

    Homework Statement prove that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is equal. Homework Equations \tau=I\alpha The Attempt at a Solution it is known that angular velocity, and hence angular acceleration about...
  15. S

    Rigid body acceleration question

    Homework Statement The illustrated equilateral triangle is supported by two links. d = 0.5 m. At the illustrated position,\dot{\theta}= 9 rad/s and \ddot{\theta}= 0 rad/s^2. Find the magnitude of a_C. http://img406.imageshack.us/img406/7264/tonguech66315yx0.th.gif The Attempt at a...
  16. C

    Optimal Length for Triple-Segment Metal Rod Hanging | Torque Equations

    Homework Statement thin uniform metal rod is bent into three perpendicular segments, two of which have length L . You want to determine what the length of the third segment should be so that the unit will hang with two segments horizontal when it is supported by a hook u <--hook...
  17. G

    Calculating Height from Work and Rotational Motion of a Rigid Body

    Homework Statement A 392-N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at 25.0 rad/s. The radius of the wheel is 0.600 m and its moment of inertia about its rotation axis is 0.800MR^2. Friction does work on the wheel as it...
  18. J

    How Do You Solve for Force B in Rigid Body Equilibrium?

    Homework Statement http://img66.imageshack.us/img66/9317/inlinelt8.th.jpg The Attempt at a Solution Sorry, By and B should be in lbs, not lbft http://img141.imageshack.us/img141/9320/pictarsp4.th.jpg My work just shows how I attempted to find the force B. According to my book, the force B...
  19. A

    Rigid Body Dynamics: Calculating Force on Beam Supports

    Homework Statement A 3.0 m long rigid beam with a mass of 130 kg is supported at each end. A 65 kg student stands 2.0 m from support 1. How much upward force does each support exert on the beam? http://i241.photobucket.com/albums/ff4/alg5045/p13-56.gif Homework Equations The...
  20. 9

    Rigid Body Kinetics Homework Solution

    Homework Statement The problem is shown in the attachment. Homework Equations Mo = Ia MgL/2 = moment of inertia of the bar Io = Ig + md^2 parallel axis theorum The Attempt at a Solution I found the moment of inertia of the bar about its center of mass: MgL/2 = (4.6*9.81*1.3)/2...
  21. K

    Calculating impulse due to rigid body collision with friction

    I am programming a simple physics simulation and have been following along with some books about the subject. Everything has gone well so far, although at the moment I'm stuck on how to calculate the impulse when two rigid bodies collide. I'll explain the algorithms that I'm using below...
  22. C

    Dynamics Problem, Relative velocity of rigid body in planar motion

    http://wps.prenhall.com/wps/media/objects/3076/3149958/studypak/questions/html/Ch16/9e_16_43.html That is the image of the problem, which includes a solution. PROBLEM- Besides being really confused on their work, the solution they give and the solution in the back of my book are both...
  23. C

    Dynamics Question, Planar rigid body/ Relative velocities

    http://wps.prenhall.com/wps/media/objects/3076/3149958/studypak/questions/html/Ch16/9e_16_43.html That is the image of the problem, which includes a solution. PROBLEM- Besides being really confused on their work, the solution they give and the solution in the back of my book are both...
  24. Y

    Angular velocity of rigid body

    Homework Statement Description of a rigid body having an angular velocity w(t) = (cos(t), sin(t), sqrt(3)) How does a movement of a rigid body having this angular velocity looks like? For instance, what would be the course of a point p=(0, 0, 1) on this body? Homework Equations r the...
  25. S

    What are the frequency and maximum velocity of a wheel rolling without slipping?

    Homework Statement W = 20 lb k = 50 lb/ft r = 4 in. Initially displaced 0.5 in. Determine the frequency and maximum velocity of the wheel (which rolls without slipping). Homework Equations (theta) double dot + (w^2)theta = 0 (x) double dot + (w^2) (x) = 0 t = 2*pi / w...
  26. B

    Solve Rigid Body Problem: Uniform Disc Mass m Falls from Theta=60°

    Homework Statement Uniform disc, mass m, falls from position where theta 60 degrees. (P is a fixed point on rim of disc). Calculate the components of thrust along and perpendicular to GP on the smooth hinge at P when theta = 30degrees. see attatched image for diagram Homework...
  27. E

    What is the method for calculating moment of inertia for basic geometric shapes?

    Homework Statement I want to calculate the moment of inertia of a 2d triangle. Let's say we've got a triangle with sides of 20 units. So it has width 20 and height 17,32. Also, let's say this triangle has a mass of 173.20 mass units (just used the surface). Now I want to calculate the...
  28. P

    Rigid Body: Rotation of a coordinate axes made up of rods

    Homework Statement A rigid body consists of three uniform rods each of mass, and length 2a, held mutually perpendicular at their midpoints (choose and axis along the rods). a) Find the angular momentum and kinetic energy of the body if it rotates with angular velocity w about an axis...
  29. S

    Fluids in Rigid Body Rotation

    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...
  30. S

    Using Navier Stokes for rigid body with constant angular speed

    I've seen several examples of using Navier Stokes in a rotating container where gravity is purely in the Z direction. These solutions generally used cylindircal coordinate systems. I wanted to attempt this problem where the gravity vector does not point purely in the Z direction. (ie...
  31. B

    Learning Rigid Body Physics with examples?

    I would like to program some rigid body physics but my maths is a lot rusty. (for example I have done differential equations at uni, but forgot everything) I cannot quite seem to get my head around the equations in 3D, with simple euler method, and quaternions. Any suggestions for learning...
  32. P

    Calculating Linear Momentum of a System with a Bullet and a Rod Collision

    Homework Statement a rod with mass 'M' and length 'L' is pivoted about a frictionless axle through it's end .a bullet with mass 'm' and speed 'v' is shot and sticks to the rod a distance 'a' from the axle. I need to find the LINEAR momentum of the system just after the hit. Homework...
  33. S

    Do All Points on a Rotating Rigid Disk Experience Centripetal Acceleration?

    Does a rotating rigid disk, for example, feel centripetal acceleration at each point of its body? or more general: Is centripetal acceleration only for non-rigid bodies? (ball on a string, ex)?
  34. M

    Two Problems on Rotation of a Rigid Body

    the first and the second:
  35. O

    How Do You Prove the Angular Velocity in Rigid Body Motion?

    Homework Statement Consider a thin homogeneous plate with principal momenta of inertia I1 along axis x1, I2>I1 along x2, I3 = I1 + I2 along x3 Let the origins of the x and x' systems coincide at the center of mass of the plate. At time t=0, the plate is set rotatint in a force-free...
  36. L

    Solve Rigid Body Motion: Pendulum Rod & Disk Eqns of Motion

    Problem statement: Consider a pendulum consisting of two parts: a uniform rod of mass m, length l, negligible thickness and with one end fixed; and a uniform disk of mass \mu and radius \rho. The rod is moving in a plane, and the disk is attached at a point P on its boundary to the non-fixed...
  37. quasar987

    Kinetic energy of a moving rotating rigid body

    Is the kinetic energy of a (not necessarily homogeneous) rigid body in translational motion and rotating about its CM the sum of the kinetic energy if the object was still but rotating plus the kinetic energy if the object was in linear motion but not rotating? This seems highly unintuitive and...
  38. S

    Solve Rigid Body Motion: Find Angle Between Axis & Invariable Line

    I am having problems figuring out this problem. A rigid body having an axis of symmetry rotates freely about a fixed point under no torques. If alpha is the angle nbetween the axis of symmetry and hte instantous axis of rotaiton, show that he angle between the axis of rotaiton(omega) and the...
  39. V

    Rigid Body Dynamics for Video Games: Calculating Velocity Vectors

    Hi, I'm developing a video game, in which I'm making a charactar with rigid-body physics (sometimes called "ragdoll" physics). The way I've made it is probably not completely realistic, because I only use velocity vectors to calculate the position of each joint of the "ragdoll", based on an...
  40. A

    Angular momentum in a rigid body

    It might be a stupid question but I do want to make sure of that: Angular momentum of a rigid body (such as a disc) is a constant vector in the lab frame. It is a vector in the body frame too, is it constant in the body frame? I refer to simple bodies with 3D rotation such as a rotationg...
  41. L

    Rolling motion of a rigid body

    A ring of mass 2.4kg, inner radius 6c.0cm, and outer radius 8.0cm is rolling (without slipping) up an inclined plane that makes an angle of theta=36.9 with the horizontal. At the moment the ring is x=2.0 m up the plane its speed is 2.8 m/s. the ring continues up the plane for some additonal...
  42. H

    How Does Mud Impact the Angular Velocity of a Pivoted Meter Rule?

    A metre rule is freely pivoted about its centre. A piece of mud of mass 20g traveling at 5ms-1 strikes and sticks to one end of the rule so that the rule starts to rotate in a horizontal circle. If the moment of Inertia of the rule and the mud about the pivot is 0.02kgm^2, the initial angular...
  43. B

    Billiard Ball backspin (draw English) - Rigid body dynamics

    I've been presented with the following problems, and would like some help/affirmation: SITUATION: A billiard ball with mass m and radius r is in rest on a horizontal table. The ball is hit with a billiard cue the height r/3 above the table, and has the velocity v0 immediately after the hit...
  44. J

    Equilibrium of a Rigid Body Under Coplanar Forces

    I have a pretty tricky question here and I can't seem to figure it out. I just maybe need a slight hint? Both rafters are 3m long and the tie rope is tied around them 0.5m from the bottoms. I've been playing with this for quite a while now so any little hints would be appreciated. Maybe...
  45. M

    Rigid Body Rotational Motion

    Question: "A uniform rod of mass m and length 2a stands vertically on a rough horizontal floor and is allowed to fall. Assuming that slipping has no occured, write the angular velocity of the rod as a function of the angle Theta the rod makes with the vertical." WORK DONE: Ic = (ml^2)/3...
  46. G

    Why VB Slow?

    http://plaza.ufl.edu/sumitg/egm3400/HW6.BMP So I've gotten Vb, but no further. Any tips?
  47. G

    Please, still with rotating rigid body problem

    :cry: I am still stuck with this problem. Please, help if you can. A large, cylindrical roll of tissue paper of initial radius R lies on a long, horizontal surface with the outside end of the paper nailed to the surface. The roll is given a slight shove (V initial = 0) and commences to unroll...
  48. C

    How to calculate the moment of inertia of the rigid body?

    I don't know how to calculate the following rigid bodies with different geometries, can anybody help me? Thin spherical shell: I=(2/3)MR^2 Solid sphere: I=(2/5)MR^2 Thanks in advance.
  49. Z

    Rigid Body Dynamics - Part II

    Hello again! About my last problem (cone principal moments of inertia around top vertice), I´ve found the main moments of inertia, but I did so by integrating the moments of inertia dI o a disk rotaing about it´s diameter (1/4 ML^2, by table), and found the correct answer. But I have done this...
  50. J

    Planar Kinetics of a Rigid Body

    QUESTION: The 50 kg uniform crate rests on the platform for which the coefficient of static friction is us = 0.5. If the supporting links have an angular velocity w = 1 rad/s, determine the greatest angular acceleration they can have so that the crate does not slip or tip at the instant theta...
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