What is Constrained motion: Definition and 24 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. deuteron

    Constraint force using Lagrangian Multipliers

    Consider the following setup where the bead can glide along the rod without friction, and the rod rotates with a constant angular velocity ##\omega##, and we want to find the constraint force using Lagrange multipliers. I chose the generalized coordinates ##q=\{r,\varphi\}## and the...
  2. Ahmed1029

    I Understanding Holonomic Constraints: Common Questions and Answers

    I've got a couple of questions concerning holonomic constraint equations: 1- Suppose I've got k holonomic constraint equations for n particles, how can I be sure those are all the ones there are and I didn't miss any? I mean, in a given situation, I can be pretty sure that I've got all, but is...
  3. R

    Particle constrained on a curve

    I tried 1. using the Lagrangian method: From ##y=-kx^2## I got ##\dot y = -2kx \dot x## and ##\ddot y = -2k \dot x^2 - 2 kx \dot x##. (Can I use ##\dot y = g## here due to gravity?) This gives for kinetic energy: $$T = \frac{1}{2} mv^2 = \frac{1}{2} m (\dot x^2 + \dot y^2) = \frac{1}{2} m (\dot...
  4. mingyz0403

    Engineering Constrained Motion of 7 Masses and 3 Pulleys

    How do you set the direction for this problem? Do you look at the motion of the block? If you set right positive, does that automatically makes upward motion positive? I set right as positive and up as positive for this problem. However, my answer was wrong. Textbook solution set right as...
  5. Prabs3257

    Velocity of the center of mass in constrained motion

    I tried getting the velocity of a which by using constraint came out to be 3 and by using the eqn for vcom i got the ans as 3.5 i just want to confirm is this the correct answer
  6. H

    Complicated pulley system on an incline?

    Homework Statement Under the action of force P the constant acceleration of B is 6 m/s^2 up the incline as in figure. For the instant when B's velocity is 3 m/s up incline, what is the velocity of point C? How do I solve this using constraints? [/B] Homework Equations For a pulley system ΣT.v...
  7. V

    Constrained Motion of a Pair of Rods

    Homework Statement Homework Equations ## v = r \omega## The Attempt at a Solution Velocity of point B= ##v_B = 4 \times \omega = 4 ## m/s Since the separation between B and C is constrained to be a constant, Velocity of B along rod = Velocity of C along the rod ## \Rightarrow v_B \cos \theta...
  8. I

    Struggling with constrained motion of connected particles

    Hi everyone! Really struggling with this question here, was hoping someone could point me in the right direction? https://puu.sh/xVitw/4c0b89c576.png 1. Homework Statement Set origin to bottom right. OA is y (Which using cos(60)*R you can determine to be 0.5R). OB is x (which you can...
  9. V

    Newton's laws of motion -- finding the velocity of a Block in a pulley system

    Homework Statement Determine the speed with which block B rises in figures if the end of cord at A is pulled down with a speed of 2ms^-1 Homework Equations Given Velocity downwards at A=2m/s The Attempt at a Solution Really stuck... Couldn't even start the question solving...I know all...
  10. L

    Equations of Motion: Constrained Hybrid Dynamics

    Hi all, I've tried to figure this out for some time without luck. Hope you might be able to give some input. I've implemented a model-based dynamics software in MATLAB based on the works of Roy Featherstone's Springer book "Rigid Body Dynamics Algorithms". So, I have the EoM of an...
  11. D

    Resolving Velocity Components in Constrained Motion

    I have been having some problem resolving the velocity component along the rope. My question will be clear if you read an illustration that I encountered which is very helpful in showing my doubt very clearly. In the Fig. given below the block ##'A'## and ##'B'## are connected with an...
  12. D

    Time for Bead to Lose Contact: Solving for Friction and Tension Forces

    Homework Statement In the figure shown, friction force between the bead and the light string is ##\dfrac{mg}{4}##. Find the time in which the bead looses contact with the string after the system is released from rest. Homework Equations Weight of the bead ##(m_1)=mg## Friction acting on the...
  13. sergiokapone

    Initial acceleration of the charge

    Homework Statement Three identical charged balls of mass m and charge q bound in a triangle thread length l. One of the strands break. Calculate the acceleration of the middle ball at the initial moment. 2. Relevant equation a. Newton's laws ##m\vec a_1 = \vec F_{12} +\vec F_{13} + \vec...
  14. C

    Constrained motion with movable pulley

    Homework Statement In this, if I want the acceleration constraint between M and 2M, I write $$AM+2AB$$=LENGTH OF STRING, which on differentiating twice gives $$a_{m}=2a_{2m}$$(which turns out to be correct). However, if we look closely, the, lower end of string is FIXED to the pulley A, and...
  15. C

    Velocity of boat connected by a pulley fixed at some height

    Homework Statement A pulley fixed on a wall of height h connects a toy boat with a man on the wall. The string is pulled by the man at a constant speed u m/s. Find the velocity of boat when the string makes an angle $$\theta$$ with the water. Homework Equations The question will be more...
  16. N

    Solve Constrained Motion Question: Car Skids Off Path

    [Mentors note: Thread moved from the Classical Physics forum after it had been replied to, hence the lack of a homework template] Hey I have been trying to solve this problem for the last few days with no luck. Question: a car starts from rest at the origin and travels along the path given by...
  17. L

    Simple Lagrangian for constrained motion - please give your input

    Hello fellow PF members I was wondering how one would go about finding the lagrangian of a problem like the following: A particle is constrained to move along the a path defined by y = sin(x). Would you simply do this: x = x y = sin(x) x'^2 = x'^2 y'^2 = x'^2 (cos(x))^2...
  18. Saitama

    Acceleration of Block B in a Constrained Motion Problem

    Homework Statement Calculate the acceleration of the block B in the figure, assuming the surfaces and the pulleys ##P_1## and ##P_2## are all smooth and pulleys and string are light. (The mass of block C is m) Ans: F/(7m) Homework Equations The Attempt at a Solution I measured...
  19. Saitama

    What is the Acceleration of C in This Constrained Motion Problem?

    Homework Statement If acceleration of A is 2m/s2 to the left and acceleration of B is 1m/s2 to left, then acceleration of C is (see attachment 1) A)1m/s2 upwards B)1m/s2 downwards C)2m/s2 downwards D)2m/s2 upwards Ans: AHomework Equations The Attempt at a Solution (see attachment 2, I hope the...
  20. C

    Constrained Motion Problem: Understanding the First Step in the Solution

    Homework Statement See attached picture.Homework Equations The Attempt at a Solution I have the solution, but I'm puzzled by the first step in their solution, which reads Xa^(2) + Xb^(2) = L^(2) The solution provider then takes the time derivative of this expression which then produces...
  21. A

    Understanding Different Accelerations in Constrained Pulley Motion

    could you please tell me how can the accelaration of masses m1 and m2 can be different. i am in a great necessity.so please explain me how can the two strings of the two sides of the lower pulley have different accelarations?
  22. A

    Velocity of Pulley and String in Constrained Motion

    how to make the velocity of a pulley work in the constrained motion of a string? my inference is that how is the velocity of the pulley associated with the velocity of the string?
  23. M

    Constrained motion question (using moments of inertia/energy)

    I've attached a screenshot of the question. This is what I've tried so far: I've calculated the initial energy of the system (which is all potential energy): Energy of disc: 0.5*I*w^2 + 0.5 *m*v^2 + m*g*h = 0 + 0 + 0 Energy of arm: 0.5*m*v^2 + m*g*h = 0 + 4*9.81*1.5Cos(45) = 41.62...