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. D

    Rotation of rigid body in space

    Hello, I have been thinking about this for hours now but I can't seem to find a definitive answer so I hope you can help me. So here is my problem: If you exert a force perpendicular to a line through the center of gravity at distance L you will produce a torque T, that torque will rotate...
  2. I

    Problem in understanding model for rigid body

    A rigid body is usually modeled as a large collection of particles in a fixed arrangement. Being particles, they by definition have no size so they cannot undergo rotation about their own axes as that does not make sense. All kinetic equations for rigid bodies are derived from this model, and...
  3. P

    Equilibrium of a rigid body under coplanar forces

    Homework Statement The foot of a ladder rests against a wall,and its top is held by a horizontal tie rope. The ladder weighs 100 N and its center of gravity is 0.4 of its length from the foot. A 150 N child hangs from a rung that is 0.2 of the length from the top. Determine the tension in...
  4. R

    How Is Moment of Inertia Calculated for Arbitrary Axes in Dynamics?

    Homework Statement Hi, I've got a Dynamics question on moments of inertia and I'm not really sure what the question is trying to get at. The question is let R=(O,B) be a rest frame of a rigid body and let the entries in J(R) be Jij. Show that the moment if inertia about an axis through O...
  5. A

    Rigid Body Collision: Balancing Momentum and Angular Momentum

    Homework Statement Im programming physics simulation. ...rigid body collision with ball. The ball is OK, but I have to push and rotate the rigid body. I have the contact point and the velocity(v) that I would add to the bodys current velocity if I wouldn't have to rotate it. So I need to...
  6. fluidistic

    Rigid body (mass sliding over a cone)

    Homework Statement There's a problem that I don't even know really where to start. It seems extremely complex to me. Basically there's a reverted cone of mass M with a mass of mass m that can slides over it without friction. But there's a constraint of motion for the particule, it must stay...
  7. S

    Rigid Body Static Equilibrium. Find force components

    Homework Statement Pin C joins members ABC and CDE Homework Equations Sum of moments at a point = 0 Sum of vertical forces = 0 Sum of horizontal forces = 0 Weight of triangle acts as a force at its centroid (1/3) its length according to this figure. The Attempt at a Solution...
  8. fluidistic

    Rigid body -badly worded problem -

    Rigid body -badly worded problem :( - Homework Statement Consider a symmetric trompo in a uniform gravitational field, with its inferior point fixed. a)Write down the Lagrangian. Determine the conserved quantities and from them study the motion of the body. b)Determine the stability...
  9. C

    Best Rigid Body Dynamics Books for Aerospace Engineering Students | Reviews"

    Hi there! It is the first I post here! Amazing Blog! Well, I am studying Aerospace Engineering. Third Year. However this semestre I intend to repeat the course on Rigid Body Dynamics ( second year) , as I think it is very, very important to fully understand these topics. So, I am...
  10. E

    Can a Hypothetical Perfectly Rigid Body Transmit Forces Faster than Light?

    Sorry in advance if this is a ridiculous question, but I've always wondered about this. Let's say we could create a wire in space away from any gravitational affects. Make the wire 2 light seconds long, for example. If we pulled on one end, when would the effects be felt on the other end? I'm...
  11. E

    Linear velocity of rigid body with vectors

    Homework Statement A rigid body is rotating with angular velocity 2 rad/s about an axis in the direction of the vector (i + j + k) and passing through the point Q = (0, 1, -1) on the body. Find the linear velocity of the point P = (1, 0, 1) on the body. (You may use the result v = ω x...
  12. N

    Simple rigid body collision reaction

    Simple rigid body collision reaction (Newton III) Hi everyone! I'm writing a physics engine as part of a game I'm making. Up until this point I've implemented inter object collisions in a rather quick and dirty manner. Whenever something moves into something else, it is simply teleported back...
  13. B

    Does Force Applied to Rigid Body Produce Equal Effect?

    a force is applied at a arbitrary point in a rigid body. Does another force equal to it and parallel to it applied to it another point produce the same effect?
  14. A

    Rigid Body Dynamics: balls colliding

    Homework Statement I want to analyse two colliding balls, rolling flat on a billiard table. I have recorded two collisions from above the table. A 1D collision and a 2D collision. In both collisions only 1 of the balls are rolling before the collision. Known is: mass of the balls: m1=207g...
  15. D

    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...
  16. A

    Difference between different kinds of motions of a rigid body

    Hi i want to know what the difference between general plane motion and rotation about fixed axis is? im using their formulas for work and energy study and as far as i see their general equations are the same. how do i identify which is which. also in a disk with planar motion, is the...
  17. L

    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...
  18. C

    Correspond Momentum of a rigid body to rotational forces

    1. Homework Statement : I have the momentum acting on the center of mass of a rigid body consisting of 3 bodies. I would like to have the corresponding rotational forces (of this momentum) on the 3 bodies. 2. I derive the general form: Frot_i= Inertia_i*(RixM)/Total_Inertia*(Ri)^2...
  19. C

    Angular velocity of a 3D rigid body with Eulerian Angles

    Say I have an odd shaped rigid body in pure rotation. I fix an orthogonal x-y-z coordinate system to the body, and coincide the origin of this coordinate system to the origin of my global coordinate system X-Y-Z. I have 3 Eulerian angles (as functions of time) which I can use to describe the...
  20. V

    Equilibrium of a Rigid Body, a boom of a crane

    Homework Statement The boom in the figure below weighs 2600 N and is attached to a frictionless pivot at its lower end. It is not uniform; the distance of its center of gravity from the pivot is 35.0 % of its length. Homework Equations Find the tension in the guy wire. Find the...
  21. J

    Rigid Body Reel and hanging mass.

    Homework Statement An object with a mass of m = 5.4 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.265 m and mass of M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown...
  22. H

    Finding the Time for Mass 1 to Hit the Floor in a Rotating Rigid Body System

    Homework Statement The two blocks in the figure are connected by a massless rope that passes over a pulley. The pulley is 14cm in diameter and has a mass of 2.4 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.54 Nm . Homework Equations so m1 = 4.0kg m2= 2.0 kg M...
  23. V

    Integrating Euler's equations for rigid body dynamics with Euler's Method

    Hello, I am trying for a couple of hours now to integrate these equations ( http://en.wikipedia.org/wiki/Euler%27s_equations_%28rigid_body_dynamics%29 ) with the Euler's method: \dot{f}=\partial{f}/\partial{t}\cong\Deltaf/\Deltat=(f(t+\Deltat)-f(t))/\Deltat . I am trying to do this...
  24. T

    Two forces; 2d rigid body, only one resultant known

    Homework Statement Two forces P and Q are applied as shown to the corners A and B of a square plate. Determine their magnitudes P and Q and the angle (weird B) knowing that their resultant R has a magnitude R = 120 N and a line of action passing through O and forming an angle of 30 degeres...
  25. R

    Trajectory of a rigid body with two wheel with different speed

    Hi, first sorry for my bad English, I am more skilled to read than to write in English I don't know if this is the right section for this topic. The problem is described in the title of the topic. My guess is that each of the two wheels goes on with circular trajectory around a same...
  26. A

    Explaining Rigid Body Movement with 15*3*10^8m Stick

    Assume a stick of length 15*3*10^8 metre. One end points towards me, at the other end we place a ball very near to the end of the stick. If i push the end pointing towards me with some force, instantaneously the ball will be moved(~). At the same time, a light beam emanating...
  27. G

    Planar Kinematics of a Rigid Body

    Homework Statement Due to an increase in power, the motor M rotates the shaft A with an angular acceleration(α=0.06θ^2) rad/s^2, where θ is in radians. If the shaft is initially turning at ω =50 rad/s, determine the angular velocity of gear B after the shaft undergoes an angular displacement...
  28. K

    How Does Skidding Affect Angular Acceleration on a Rotating Turntable?

    Homework Statement A turntable rotates at a uniform angular speed of 3.0 rads^-1. A record is dropped from rest onto the turntable. Initially the record skids on the turntable but eventually rotates together withe the turntable. (a) While the record is skidding on the turntable, the angular...
  29. W

    Find resultant of multiple torques on a single rigid body

    hi I have multiple torques acting at different points on a rigid body I want to find the resultant force and torque (about the body CM) I think I can see how to "convert" an off-center torque to a torque + translation using the parallel axis theorem - but am wondering if there is a...
  30. J

    Ansys Rigid Body Motion - Static Structural

    I am and have been trying to do a specific simulation for the last several weeks. It seems like I take one step forward two steps back. See below: See the attached files. I'm on Ansys Workbench 13. [PLAIN]www.plastics-consulting.com/rod.stp[/URL]...
  31. fluidistic

    How to Calculate the Kinetic Energy of an Inhomogeneous Cylinder?

    Homework Statement I think the problem was taken out from Landau&Lifgarbagez's book on classical mechanics. An inhomogeneous cylinder of radius R rolls over a plane. The mass is distributed in such a way that a principal axis is parallel to the rotational axis of the cylinder and the center of...
  32. C

    Help me solve my dilema.Kinematics and dynamics of Rigid body problem.

    Homework Statement Find acceleration-x ̈ of the load. Force F=10G, friction μ=1/3, mass of he body is G. I tried two ways of solving this problem but not sure if any is good. I think second is good. But wondering if first is also good? Homework Equations Ek=1/2 G/g x ̇^2 Fμ=G μ The...
  33. fluidistic

    Rigid body kinetic energy+ constraints (upper level classical mechanics)

    Homework Statement Using the corresponding constraints conditions, calculate the kinetic energy of 1)A homogeneous cylinder of radius a that rolls inside a cylindrical surface of radius R>a.Homework Equations My toughts: I hope they meants "roll without slipping". Let's consider this case...
  34. fluidistic

    Classical mechanics, principal moments of inertia of a rigid body

    Homework Statement Determine the principal moments of inertia of a circular cylinder with radius R and height h. Homework Equations Not sure. The Attempt at a Solution This is the first problem of this kind I attempt to solve. From what I've read on wikipedia, the tensor of...
  35. S

    Work/ energy on a rigid body (mechanics)

    pls see attached file for the question. so W = change in T + change in Ve + change in g T = 1/2 mv2 + 1/2 I (w1^2 - w2^2), but how do u find the velocity, shouldn't it be 0 since it starts/stops at v=0. for Ve = 1/2 kx2, how do u know how far it stretches once the moment is applied? :O :(...
  36. S

    Solving Rigid Body Kinetics: Pulley Tension & Moment of Inertia

    hey guys, please see the attachment for the question. i drew FBDs and everything. i want to know a few things tho. how do i calculate the tension in the pulley? if they'd given me acceleration i could have used T-mg =ma. but they havent. also once the Tension is found, do i just find the...
  37. H

    Understanding the Center of Mass in a Hemispherical Bowl in Equilibrium

    I know and understand why the c of m of a uniform hemispherical shell (i.e a hollow hemisphere) is r/2 on the axis of symmetry (where r=radius of shell). I looked at the solution of the following question and still don't understand. Question: A hemispherical bowl, which may be modeled as a...
  38. W

    Period of Small Oscillations for Rigid Body Pendulum

    Homework Statement A pendulum consists of a light rigid rod of length 250mm, with two identical uniform solid spheres of radius 50mm attached one on either side of its lower end. Find the period of small oscillations (a) perpendicular to the line of centers, and (b) along it.Homework Equations...
  39. G

    The moment about points in a rigid body

    If a rigid body has a net moment e.g. rotating clockwise at 2Nm moment about the centre of mass, does every point on the body have 2Nm moment? Or just the point at the centre of mass have a net moment? Thanks
  40. S

    Dynamics: Rigid body problem, angular rotation

    Homework Statement An L-shaped plate is pinned at a point F and G with two poles OF and ED (OF = 1m, OG = 0.6m), which in turn are pinned at fixed points O and E, respectively, as shown in the attached image. If rod OF rotates with a constant angular velocity 0.2rad/s counter-clockwise, when...
  41. Telemachus

    Rigid body kinetics in 3 dimension space

    I need some help with the equation of moments for this exercise: Each wheel of an automobile has a mass of 22 kg, a diameter of 575 mm, and a radius of gyration of 225 mm. The automobile travels around an unbanked curve of radius 150 m at a speed of 95 km/h. Knowing that the transverse distance...
  42. S

    Rigid Body - Linear (Center of Mass) motion/Rotational Motion

    Homework Statement This is a very simple problem to state, yet I've not found any answers on PF or anywhere else online. So let's say we have a simple rigid body like a rod. We apply an external force Fext for a fixed time dt to the rod in two different ways: (1) directly on the center of...
  43. R

    Inertia, rigid body motion and angular momentum problem

    1. A uniform thin rod of weight W is supported horizontally by two vertical props at its ends. At t=0 one of these supports is kicked out. Find the force on the other support immediately thereafter - it should be in terms of W. 2. Homework Equations : I=M(L^2)/12 3. Don't even...
  44. I

    Mechanics (general motion of a rigid body)

    Homework Statement The bicyclist applies brakes as he descends a track making an angle β with a horizontal direction. The front wheel of the bike locks and starts to slip along the incline. Find the magnitude of the decleration a that would cause a dangerous condition of tipping about the...
  45. S

    Calculating Inertia and Radius of Gyration for a Rolling Object

    Right, I need to find out the Radius of gyration of an object as it rolls down a ramp... So I've got the equation K=r square root((g.t^2 sin theta/ 2x) -1)) These are the numbers I have... Object A R = 0.004 g = 9.81 t = 16.45 theta = 5.31 x = 0.66 I got an answer of...
  46. D

    Vibration related: Rigid body modes

    Hi, everyone. I'm required to complete an open ended analysis of the following problem: http://imagefrog.net/show.php/146581_image.png http://imagefrog.net/show.php/146581_image.png I'm not requesting a solution, I'm only looking for assistance in relation to determining the spring stiffness...
  47. Z

    Finding the Velocity for Zero Hinge Force in Rigid Body Collision Problem

    Homework Statement A uniform rod of mass M and length l is hinged at point O as shown in fig. A small particle of mass M/3 strikes the rod with velocity v at a distance 3l/4 from O and sticks to it. Find the value of v such that the force exerted by the hinge on the rod just after the impact...
  48. P

    Will a Rigid Body Continue to Rotate Without Centripetal Force?

    Homework Statement hello, I need help with projection of a rigid body with moment of inertia I, the rigid body was earlier moving on a circle of R radius with \omega angular velocity and was making angle of \alpha when centripetal force stopped to work. And I need to know if this rigid body...
  49. Telemachus

    Help with Rigid Body Exercise: Determine Speed of B

    Homework Statement Hi there, I'm starting with rigid body, and I'm having some trouble with it, so I'll need your help :D I have this exercise now, but I will probably come with some others later. The exercise says: The collars A and C glide along the vertical rods and B of the horizontal. If...
  50. S

    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...
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