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. R

    How Does Distance r Influence Angular Velocity in Rigid Body Dynamics?

    Need help! Rigid Body Dynamics Homework Statement I'm having problem with the following problem. The encircled portion of the figure is giving me trouble. I am getting confused on how to correlate it with reference frame oxyz. please help. It's urgent.. :( what is the significance of...
  2. C

    Question about two torques on rigid body.

    Hi, here's the question: A massless, rigid rod has motors attached on each end. The motors are each connected to a massive disc, and the motors accelerate the discs in the directions indicated by the arrows. Due to the torque from the each motor on its disc and hence that on the rod and...
  3. C

    Kinematics and rigid body simulation

    Hello, I have a question regarding how I'm simulating motion using the common time integrating approach to simulating rigid bodies. I have net forces and solve for position from those: acceleration = force / mass velocity = initial velocity + acceleration * time position = initial position...
  4. H

    Rigid body rolling along an inclined plane

    Homework Statement So rigid body (ring, cylinder, sphere), who's radius of gyration is known, rolls down an inclined plane without slipping. Find velocity as a function of height. m - mass of the body. y0 - initial height, g - gravitational acceleration, v - speed. I - moment of inertia, K -...
  5. G

    Planar Kinematics of a Rigid Body

    Homework Statement A truck is moving to the right with a speed of Vo=12km/h=3.3333m/s while the pipe section in its bed has a radius R=1.25m and a center at C that rolls without slipping over the truck's bed. The center of the pipe section C is moving to the right at 2m/s relative to the...
  6. G

    Planar Kinematics of a Rigid Body

    I have been given the following problems for practice for an upcoming test that is going to have similar problems on it. I was wondering if someone knows how to do them as I want to make sure that I know how to do them correctly so I will be prepared come test time. Thank you!
  7. S

    What Is the Angular Velocity of a Complex Rigid Body Assembly?

    Homework Statement The rigid body assembly is made from a 15 Kg disk, an 8 Kg slender rod, and a small 4 Kg sphere. The radius of the disk is R = 0.4 m and the length of the rod is L = 1.2 m. The pivot O is at the center of the disk. The assembly is released from rest at the horizontal...
  8. P

    Solving Rigid Body Dynamics: Find Tension in Cable A

    Not really sure if this is where this should be but oh well. 1. Homework Statement It is given that: b = 200 mm mass = 6 kg Find the tension in cable A immediately after cord B is cut. 2. Homework Equations Moment = I*alpha + m*a*d F = ma? 3. The Attempt at a...
  9. P

    What Is the Tension in Cable A After Cord B Is Cut?

    Not really sure if this is where this should be but oh well. Homework Statement Image attached. It is given that: b = 200 mm mass = 6 kg Find the tension in cable A immediately after cord B is cut. Homework Equations Moment = I*alpha + m*a*d F = ma? The Attempt at a...
  10. R

    How Does Angular Acceleration Affect Block Movement on a Rotating Plate?

    sorry someone can help me with this problem about the revolutions of the plate?? thanks! A small block B rotates with the horizontal plate A in Fig. the distance between the block and the axis of rotation is r = 100 mm, the angular acceleration of the plate is α = 2 rad/s2 =...
  11. Amith2006

    Principal axes of a rigid body

    It is a known fact that every rigid body has a set of orthogonal axes called principle axes about which when rotated the angular momentum vector and the angular velocity vector point in the same direction. Inside the body we can take any point as the origin and find a combination such that the...
  12. F

    Rigid Body Momentum - Calculate Velocity

    Rigid Body Momentum? Homework Statement **** PICTURED IS ATTACHED *** The center of the homogeneous disk of mass m shown below has an initial velocity of v0 up the slope. Find the velocity of the disk after an elapsed time of !t, assuming that the disk rolls without slip. Use...
  13. S

    Rigid Body Motion - cylinder on a plane

    Homework Statement Pretty picture: I am currently stuck on #1. Homework Equations Not exactly sure but... For #1, I assume the relevant equations are those relating the (i) gravitational force to momentum and (ii)torque due to gravity to angular momentum: (i) F = dP/dt (ii) K = dM/dt...
  14. H

    Rigid Body Motion: Sphere on Inclined Plane

    Homework Statement A sphere of mass M and radius R it`s given a velocity Vo on the base of a inclined plane (theta being the angle) and friction coefficient mu (you may assume that static and kinetic friction are equal) Find the position of the ball as a function of time Homework...
  15. 3

    How Do You Calculate Velocity and Acceleration in a Belt and Pulley System?

    Homework Statement Three belts move over two pulleys without slipping in the speed reduction system. Point A on the input belt moves to the right with a constant spped of 0.6m/s. Determin the velocity of point C on the output belt, and the acceleration of point B on the output pulley...
  16. Z

    Elevator Question (Rotation of rigid body and Energy)

    Homework Statement An elevator system in a tall building consists of a 710 kg car and a 810 kg counterweight, joined by a cable that passes over a pulley of mass 280 kg. The pulley, called a sheave, is a solid cylinder of radius 0.700 m turning on a horizontal axle. The cable has comparatively...
  17. P

    Rigid Body dynamics - elastic collisions

    Homework Statement A uniform rectangular tile drops without spinning until its corners reach positions (0; 0; 0); (2a; 0; 0); (2a; 2b; 0); (0; 2b; 0), when it strikes the top of a vertical pole at a point very close to the (0; 0; 0) corner. Just before impact the velocity of the tile was...
  18. Z

    When to use different kinetic energy equations

    hi, when will i use 0.5mv^2 and when will i use 0.5Iw^2 when will i use both? as far as i can see one represents the movement of the center of mass and the other the angular movement. so as far as i understand for a moving cylinder i would use the sum of those. but i can't think of any...
  19. Z

    What Is the Angular Velocity of a Hinged Stick After Collision?

    hi, i am trying to solve this question. A thin stick of mass M = 4.9 kg and length L = 2.6 m is hinged at the top. A piece of clay, mass m = 1.0 kg and velocity V = 4.9 m/s hits the stick a distance x = 2.20 m from the hinge and sticks to it. What is the angular velocity of the stick...
  20. Y

    Research on rotational of rigid body.

    My teacher ask us to do a research on physics. I have been choose a topic of torque. I need to find a problem statement before i can start my research. My problem is i have no idea on problem statement. Can somebody help me? ASAP!
  21. Z

    How Do You Calculate the Speed and Spring Constant of a Pivot-Mounted Rod?

    hi, i'll be glad to get some help with that. thanks A thin uniform rod has mass M = 0.5 kg and length L= 0.55 m. It has a pivot at one end and is at rest on a compressed spring as shown in (A) in the attached image. The rod is released from an angle θ1= 63.0o, and moves through its...
  22. S

    Dynamics: planar kinetics of a rigid body (impulse and momentum)

    Homework Statement http://img340.imageshack.us/img340/7379/87835960.png r_{i}=.3 m \text{ and } r_{o}=.9 m The spool has a weight of 300N and a radius of gyration k_{O} = .45 m. A cord is wrapped around its inner hub and the end subjected to a horizontal force P = 50N. Determine the spool's...
  23. S

    Looking for proof that a free rigid body will rotate about its CM

    Can anyone recommend a textbook or web paper that proves that, in general, a free rigid body will act in the following way when the body is subjected to a force (or impulse) that is torque producing: a) The center of mass (CM) moves in a straight line. b) The body rotates about an axis through...
  24. C

    Simple Harmonic Motion of a Rigid Body

    Homework Statement A very light, rigid rod with a length of 0.570 m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. Determine the period of oscillation. Homework Equations omega =...
  25. P

    Planar Kinematics of a Rigid Body (Relative Motion Analysis using Rotating Axes)

    Let me start by saying thank you to any responses I receive. I understand the methods for solving this problem but I have concluded that either part or all of my solution is incorrect. After solving for the angular velocity, I differentiated my answer in order to check the angular...
  26. A

    Rigid Body Equilibrium Question

    Hi, I have a question regarding Equilibrium problems. Here is the example of my hw. Find the tension T in each cable and the magnitude and direction of the force exerted on the strut by the pivot. I know how to find T. The only problem is i couldn't imagine the force exerted on the strut by the...
  27. B

    Can a Rigid Body's Rotation Be Described with Only Two Successive Rotations?

    I try to clearify it as much as I can, and I greatly appreciate the given answers. Suppose that we have a rigid body. We attach a movable coodinate frame on this body. Normally, if I perform 3 successive rotations such as Z-Y-X or Z-Y-Z (or any other 24) I can describe its rotation in...
  28. Y

    Kinematics of a Slender Bar with Constrained End Rollers

    Homework Statement The small end rollers of the 3.6 kg uniform slender bar are constrained to move in the slow, which lies in a vertical plane. A the instant theta=30 the angular velocity of the bar is 2 d/sunter-clockwise. Determne the angular acceleration of the bar,k the reaction at A and...
  29. Y

    How Much Vertical Acceleration Can a Forklift Give Without Tipping?

    Homework Statement The forklift and operator have a combined weight of 50,000 N and center of mass at G. If the forklift is used to lift the 10,000 N concrete pipe, determine the maximum vertical acceleration it can give to the pipe so that it does not tip forward on its front wheels...
  30. H

    Rotational kinetics of a rigid body

    Hi, I had a question about a dynamics problem involving the rotation of a rigid body. Here's what I've worked out so far, but I can't seem to get the correct answer. I'm suppose to find the magnitude of the reactionary forces at pin A. See the fbd for a drawing of the problem. I'm not sure if...
  31. A

    Rigid Body Kinetics Homework Help - Solving Equations & Finding Answer

    Homework Statement Homework Equations \SigmaM = I\alpha \SigmaF = ma The Attempt at a Solution I have made an attempt at this problem, it can be seen in the image below. I think I have done everything correctly, but my answer is incorrect. Any help would be greatly appreciated.
  32. T

    Rigid body solid: center of mass and tendency to topple

    Homework Statement A whimsical piece of furniture has the base shaped like a star. Formulate the condition in terms of the location of the center of mass of the object that the piece would not topple over. A sketch would be helpful. The Attempt at a Solution Can someone help me...
  33. F

    Understanding Weight Distribution on Beams: The Role of Rigid Body Moments

    how are weights distributed on a beam
  34. M

    Rigid Body Equilibrium problem (no calculus)

    Homework Statement Consider a gymnast on a bean placed on upright posts. The beam has a mass of 10kg and the gymnast has a mass of 50kg. The beam is 5 meters long, and the gymnast is 1 meter from the right side. The gymnast may be treated as a particle. Find the force exerted by each...
  35. R

    Paradox of Rigid Body: Solve the Mystery

    There is a rod treating as rigid body, the rod which mass is m and lenghth is R rotate about one end of itself with the angular acceleration \alpha . Apply a tangential external force f on another end to make the rod rotate. Now divide the rod into elements of mass. For each mass element dm with...
  36. A

    Determining the angular and linear accelerations of a Rigid Body

    Hello, all! I am currently working with the governing equation of a rotating, translating rigid body. That is: \vec{a_i} = \vec{a_c} + \vec{\alpha} \times \vec{r} + \vec{\omega} \times \left( {\vec{\omega} \times \vec{r}} \right) Where a_i is the linear acceleration of some point...
  37. F

    Calculating Forces on a 2D Rigid Body Held by Two Points

    This isn't homework, it's for a simple computer program I'm trying to write. It's been a long time since I took a physics class, but I seem to remember getting homework questions like this. http://www.imagechicken.com/uploads/1244655138002459200.png If I have a 2D rigid body, I know its...
  38. S

    Mechanics Book on 3-D Rigid Body Motion

    Hi guys, I'm going to university this fall and am preparing this summer for the physics courses I will be taking. I have Kleppner and Kolenkow's mechanics book, and things were going smoothly until I hit the problems in chapter 7 on rigid body motion in three dimensions. In this chapter, topics...
  39. M

    How to show that motion of a rigid body = translation + rotation

    We all learn in the introductory mechanics class that the motion of a rigid body can be composed of a rotation and a translation. But how can one prove this? I mean: Let us have some rigid body in two configurations in space, how can I show that I can transform one configuration to another by...
  40. E

    Rigid body dynamics: Resting contact

    I'm currently programming a 2D rigid body dynamics engine. While I have realistic collision detection and response between polygons, I have trouble in the simulation once I implement gravity. When these rigid bodies are influenced by gravity, they never fall to complete rest (e.g. they...
  41. C

    Understanding Moment Equations in Rigid Body Equilibrium

    I have uploaded the question with solution at this address: http://i41.tinypic.com/o5xm5j.jpg All I need to know is why in the moment equation "NA*a - F*b = 0" the forces Nb and Nc aren't included. Is it because the moment is being calculated about the dot in the middle, and the other two...
  42. M

    Rolling motion of a rigid body problem

    1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping 2. The attempt at a solution I found V first. V= rw =...
  43. T

    How to Solve for Radial Component in Rigid Body Rail Problem?

    here is the question and how i tried to solve it http://img242.imageshack.us/img242/7320/83882436ug7.th.gif
  44. fluidistic

    Rigid body/ force applied on a wheel

    Hi PF, I'm a bit disappointed because the final exam is coming up next Monday and I can't solve this problem. Not that I don't know how to proceed, but I just get a wrong answer. Homework Statement See figure to imagine the situation. This is about a wheel of radius R which contains a circle...
  45. J

    What Are the Effects of Rigid Body Force and Torque?

    I have no idea what the solution to this problem is and would appreciate if someone pointed me in the right direction.
  46. W

    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...
  47. fluidistic

    What is the motion of a physical pendulum with a rotating rigid body?

    Homework Statement Hello, I've tried all I could and get very confused about how to approach the problem. Here it comes : A disk of mass M and radius R can rotates around an axis passing by the point A without friction situated on its circumference. The disk is in a vertical plane. We let...
  48. W

    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...
  49. A

    Is a Rigid Body Always Concentrated at its Center of Mass in Circular Motion?

    When considering pure rotation of a rigid body about some point , then can we always consider the body to be concentrated in its centre of mass and use all force related equation treating it like a point object situated at it center of mass.? Why? Can anyone prove mathematically because there...
  50. A

    Confusing ROTATIONAL RIGID BODY QUESTION problem conceptualizing

    Homework Statement A piece of cloth with irrelavent mass is wrapped around a 67.5 kg cylinder of radius 0.167 m. Joe holds the free end of the cloth. The cylinder is released from rest, and Joe pulls the tape upward at a speed that just prevents the center of mass of the cylinder from falling...
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