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. BroPro

    Angular momentum of rotating hoop

    Problem: Official solution: My calculation: \begin{align*} \mathbf L &= M \mathbf R \times \mathbf V + \mathbf L_{cm} \\ &= M R (\hat j + \hat k) \times (- \Omega R \hat i) + MR^2 \Omega \hat j \\ &= MR^2 \Omega (\hat k - \hat j + \hat j) \\ &= MR^2 \Omega \hat k \end{align*}
  2. Hak

    Drawing an irregular rigid body on GeoGebra

    I will preface this by saying that I am not very knowledgeable about computer software and programs, so far I know the basics. I want to draw an irregular rigid body on GeoGebra, maybe using commands like "Freeform," but I haven't found a way yet. What do you recommend? Thanks to those who would...
  3. P

    Rigid Body Problem Involving a Tilted Rotating Disc

    Using these equations, I find L=0.02Nms, I=0.02Kgm^2 and KE=10mJ However, i don't think that this is the right method here.
  4. chris25

    Fictitious forces on a rigid body

    I was confused by how to work this problem in a rotating frame. The solution read that the centrifugal force on the mass should be of magnitude 𝑚𝑤𝑅^2. However, I thought it would be 𝑚𝑤𝐿^2 where L is the distance between the mass and the center of the circle (L = l + R). What am I missing here?
  5. L

    Moment of inertia of a uniform square plate

    I placed my Oxy coordinate system at the center of the square, the ##x##-axis pointing rightwards and the ##y##-axis pointing upwards. I divided the square into thin vertical strips, each of height ##h=2(\frac{L}{\sqrt{2}}-x)##, base ##dx## and mass ##dm=\sigma h...
  6. A

    I Rigid body mechanics and coordinate frames

    Hello all, I have some issues understanding the inertial-frame (or global-frame, G-frame) versus the body-frame (B-frame) when it comes to simulating the motion of a rigid body in 2 dimensions (planar body mechanics) in a system of ODEs. I have been self-learning from textbooks on simulating...
  7. A

    I Rigid body physics (machine learning environment)

    I guess that the reason that objects fall over is that there is nothing to hold it's center of mass. So what I want to do is to work out how fast in Delta intervals it would rotate and fall over.
  8. J

    I Angular momentum of an atom within a rigid body in motion

    Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion? My intuition is that, whether considered in a classical sense or quantum sense, the speed of a given electron in its motion within an atom will be constant and...
  9. B

    Existential dilemma on angular velocity of a complex rigid body

    I assumed the angular velocity of the center of mass of the two discs about z axis to be w1 note that angular velocity of center of mass of both discs and center of anyone disc about z axis is same, you can verify that if you want, me after verifying it will use it to decrease the length of the...
  10. Uchida

    Conservation of Linear Momentum of Rigid Body

    I solved it by two methods: ----------------------------------------------------- First, by conservation of linear momentum, using the vector velocities of each particle: In the imminence of the impact, the velocity of all the three particles are the same, \vec v_0 = - \sqrt{2gh} \hat j...
  11. wrobel

    I What Happens When a Rigid Body with a Fixed Point Moves Along a Closed Path?

    Today I read a book in mechanics and encountered a funny proposition about rigid body with fixed point. Perhaps somebody will be interested to propose it to students as a task. This proposition is almost correct:) Consider a rigid body with a fixed point ##O##. Let ##Oxyz## be a coordinate...
  12. warhammer

    Question on Moment of Inertia Tensor of a Rotating Rigid Body

    Hi. So I was asked the following question whose picture is attached below along with my attempt at the solution. Now my doubt is, since the question refers to the whole system comprising of these thin rigid body 'mini systems', should the Principle moments of Inertia about the respective axes...
  13. Pipsqueakalchemist

    Engineering Dynamics rigid body cabinet problem

    So for this question I understand part A but part B is confusing me, when using point B as the centre of the moment, I get different sign for the mad term. If you take clockwise as positive than 100N force and the force at point G are causing a positive moment and gravity is causing an negative...
  14. Pipsqueakalchemist

    Engineering Rigid body Newton’s law homework

    For this problem I know how to get the answers but I have a few things I’m not 100% sure about. First how do we know that the rod is experiencing centripetal motion? Second, when using moment about point G how do we know that the angular acceleration is equal to zero? And third the radius is 0.4...
  15. Pipsqueakalchemist

    Engineering Dynamics rigid body homework question

    So I’m confused about a few things in the solution. Why is it that speed of the V_h appears on both gear a and b? Is it because both gears are both in contact so they have equal speeds just in opposite direction. Same confusion for V_e being on the top of gear b. So Just because gear e doesn’t...
  16. Pipsqueakalchemist

    Engineering Dynamics rigid body question -- Velocity of points on a car's wheel

    The solutions used the spend of the wheel and its radius to find the angular velocity. I’m confused because I thought to find angular velocity you use the speed at the points of the radius not the translation speed of the wheel itself. Can someone explain this to me please
  17. Leo Liu

    Stability of rigid body rotation about different axes

    We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy. However, for this question involving a rigid body, the most stable axis is the one with the lowest moment of inertia...
  18. B

    Equilibrium of a Rigid Body: Balancing Forces and Moments

    Components of gravitational force on M: normal force:M*g*cos(90-α)M*g*sin(α) Downhill force: M*g*sin(90-α)=M*g*cos(α) On m: normal force: m*g*cos(α) Downhill force: m*g*sin(α)
  19. mastermechanic

    Rigid body kinetics -- force on ankle joint

    PROBLEM Here from the conservation of angular momentum I found angular velocity just before impact, $$ H_1 = 0 $$ $$ H_2 = I_0\omega + mV_0d $$ $$ H_2 = 66\omega + 76.(1.2).(0.87)$$ $$ H_1 = H_2 $$ $$ \omega = 1.202 rad/s $$ But I couldn't solve it to find joint force. Thanks in advance,
  20. Butterfly41398

    Rigid body rotation -- A person walking around a merry-go-round

    This one is challenging for me. Can anyone give me a hint?
  21. greg_rack

    How can the weight force of a rigid body be applied in a moments equation?

    I'm having a hard time solving this problem since I don't really know how to apply the weight force of the trap door. Ideally, in order to find the contact force exerted by the rod, I would find out the weight force of the trap in the point of contact and then find its component radial to the...
  22. Like Tony Stark

    What causes an object to rotate?

    Hi I've been taught that any force not going through the centre of mass will create torque. Consider a rod of length ##L## and negligible mass, with two balls of mass ##m## attached to its ends. Its centre of mass is at ##\frac{L}{2}##. I have two questions: 1) If a force ##F## is applied to...
  23. Like Tony Stark

    Direction of the normal force when acting on a tilted object

    My question is: given a rigid body which interacts with a surface, what's the direction of the normal force? Because, as the word says, it has to be normal to the surface. But when treating problems of a vertical rod which is slightly pushed and forms an angle ##\theta## with the surface, some...
  24. P

    I Size Limit of Accelerated Rigid Body in Irrotational Born Rigid Motion

    I was thinking - and reading a bit - about the size limit on accelerated frames, and there is an interesting and relevant result I found. If we rephrase the question from "is there a size limit on an accelerated frame" to "is there a size limit on an accelerated body in irrottational born...
  25. G

    Rigid body sliding without overturning

    My attempt: When the body is about to overturn backwards, the normal force and frictional force are applied on point A. If I want to avoid overturning, torque must be 0. Then, I calculate torque with respect to A. The value I get for h is negative, implying there is no minimum value for h...
  26. D

    (Check solution) Conceptual problem about the equilibrium of a rigid body

    Please help to see whether I did correct or wrong, thank you.
  27. K

    What was Newton's insight on rotational motion in Principia?

    mgR = d(mvR + MvR + ½M(R^2)v/R)/dt mgR = ma + Ma + ½Ma mg = a(m + 3/2M) v = mgt / (m+3/2M) My answer is incorrect. The right answer is v = mgt/(3m+M), but I have no idea what I'm doing wrong.
  28. K

    What does it mean that a rigid body is in equilibrium?

    So I have always been thinking that equilibrium means that an object is not moving or having constant acceleration. On a webside they said: " A rigid body is in equilibrium when it is not undergoing a change in rotational or translational motion. " To me it sounds like the object then must not...
  29. archaic

    Rigid body rotation problem: Mass on a cord spinning up a wheel on an axle

    (I know how to solve the problem, that's not what I am looking for.) I have a problem with how I ought to understand the moment of inertia. The only torque I see applicable on the wheel is that of the tension, and so I think that ##I## should be ##m_{\text{point}}R^2##, without including all the...
  30. A

    Magnetic fields generated by the general rotations of a charged rigid body

    The calculations for the magnetic field produced by a uniformly rotating charged sphere can be found in basically every book on electrodynamics. I wonder what happen with the magnetic fields produced by rotating rigid solid that also present precession and nutation movements. The question comes...
  31. Adesh

    I How a rigid body causes a reaction force?

    The definition of rigid body says it cannot be deformed (theoretically). Now, Newton’s third law is caused (I mean the reaction force is caused ) due to the deformation of the body. What I have learned is that every body is like a spring, when we push on it we compress it and hence feel a...
  32. E

    Is the rotational KE of a rigid body considered as internal energy?

    I'm inclined to say no, but am by no means certain. The total kinetic energy of a system of particles is $$T = \sum_{i} \frac{1}{2} m_{i}\vec{v_i}\cdot\vec{v_i} = \frac{1}{2} m_{i}(\vec{v_{COM}} + \vec{v_{i}^{'}})^{2} = \frac{1}{2}M\vec{v_{COM}}^{2} + \frac{1}{2}\sum_{i} m_{i}...
  33. Like Tony Stark

    Why Is the Reaction Force Inclined in One Case but Perpendicular in Another?

    Hi, I have a doubt about reaction forces... I've attached a picture that shows two similar situations. The first one shows a rod left with an angle ##\beta## while it is on a smooth surface. The second one shows a rod leaning on a smooth surface and wall. My question is: why is the reaction...
  34. L

    Projectile motion of a two-point rigid body

    I would like to patch some gaps in my physics background. For example, I've been trying to come up with the sollution to the following: I have a model rigid body made up of two mass points and a massless rod connecting them. I throw the body with initial velocity under some angle of elevation...
  35. O

    I Force on a rigid body inside a liquid flow

    Hi, I am trying to find out Force on a rigid body when it is completely inside a fluid with density p, i.e. the body is completely drowned in the liquid and then another liquid is pushed into the container with different density 'r' (such than r > p). Thanks.
  36. L

    Calculate the moment of inertia of this body

    I use the moment of inertia I = 1/12ml2 for an axis perpendicular and passing through the center of mass of a rod. In a cube built out of 12 rods I have 8 rods at a perpendicular distance l/2 from the axis through the midpoint of a cube. These 8 rods contribute the moment of inertia I1 =...
  37. Santilopez10

    Sign Convention for Angular Acceleration in Rotational Motion

    we know that the center of instantaneous 0 velocity lies in the interception of 2 perpendicular lines to 2 points, which in this case lies above B. The velocity of any point of the rod can be described relative to the center of instantaneuous 0 velocity ##(Q)## as: $$\vec v_{P/Q}=\vec \omega...
  38. D

    Rigid body simulation of complex mechanical systems

    Greetings, I'd like to simulate a complex mechanical automaton with lots of gears, cams, levers and springs. Most of the parts are going to be 3D printed except for some metal springs, rods and bearings. I want to make sure everything fits together and works as expected. Here is just a small...
  39. Celso

    Rigid body motion - thin disc

    Why is the gravitational potential energy of the chain's center of mass equal to the total kinetic energy of the disc after it was fully wrapped? My first thought was to write ##E_{0}=(M/2+M)g∗2πR=E_{f}= Ep## (from the chain) ##+Ec## (from the disc). Instead he wrote ## mg \frac{l}{2} ## = ##...
  40. D

    Rigid body equilibrium question

    Problem in the picture. I have a question regarding the problem in the picture. Ma=0 -2Kn*1a+By*4a=0 --> By=0,5kN Mb=0 2kN*3a-Ay*4a=0 --> Ay = 1,5kN Ax=0kN Ay is the pin support and By is the roller support. According to the solution By should be 1kN but isn't that the wrong answer? 2kN has...
  41. D

    Why Is My Rigid Body Equilibrium Equation Incorrect?

    Hello Ihave gotten as far as coming up with an equation for the sum of moments and it goes as follows: bh*1/2b-1/2hb*1/3b=0 the answer for h i get is wrong and i don't know if i am missing something. moment arm on the b is 1/2b and the moment arm on h is 1/3h because of the way water pressure...
  42. O

    Dynamics Problem: Determine Velocity and Acceleration of Rigid body

    Hello, Wanted to know if this was the correct approach to solve this example. I uploaded the question along with an attempt. Thanks in advance.
  43. P

    Intuition behind centre of mass equation for a rigid body

    So my basic understanding of an integral is that it finds the area underneath a graph. I understand the idea behind an integral being the summation of f(x) * delta x, where delta x approaches zero. If I look at the integral it's telling me that there's a change in mass that is being...
  44. A

    Rigid body mechanics, solution seems incorrect?

    I've attached the problem and solution as picture. To my understanding, the gear E and the rod OB are taken together as the rotating rigid body. However, the equations of motion and (##∑F = macm##) are applied to the center of mass of the rod, G, rather than the center of mass of the rigid body...
  45. Abhishek11235

    Euler Equations for Dynamics of rigid body

    I have been studying the dynamics of free top from Morin's book. In his book when describing the dynamics,he writes down the equation of motion as shown in screenshot. However,I am not able to understand which term refers to which coordinate system. For eg: Here ##\omega## refers to angular...
  46. M

    Rigid Body Rotation relative velocity question

    This is a question about the concepts behind rigid body rotation when we use relative velocity. In general, let us say that we have a rigid body and on it are two points, A and B, which are moving with velocities vA and vB respectively. These velocities are in random directions. The theory...
  47. F

    Rigid body kinematic motion and rotation

    Hello everyone, A rigid body is a system whose points, pairwise, always keep a constant mutual distance. Let's say the body is in a certain configuration ##C_0## at time ##t_0## (which means that each point has a specific velocity and position relative to a fixed lab reference frame) and the...
  48. J

    Rigid Body Mechanics - 2 or more bodies

    When I derive the equations of motion for 2 or more bodies where one is rotating and the other is a mixture of rotation and translation, I get a term multiplying angular velocity squared. I know its right but I don't know what to call it. Can some help me with what to call it (it means C1*ω2...
  49. JTC

    Contributions to Dynamics - China

    Hello, To ensconce this question properly, we know that some of the major contributions to the discipline of rigid body and classical particle dynamics came from: Newton, Euler, Hamilton, Lagrange and so on... (no need to suggest other western names right now - I am aware of them). However I...
  50. Clara Chung

    Question about a rigid body and energy

    Homework Statement Homework EquationsThe Attempt at a Solution I have posted the solution, but I don't really understand about the second term in the equation. Shouldn't the angular velocity of the ball be (b dθ/dt) /a instead of ( (b-a) dθ/dt )/a in the solution?
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