# 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. ### 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. ### 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. ### Two Pulleys, Two Strings and Two Blocks

Someone pls solve this. I've done it but I'm not sure if it's correct. Thanks!

17. ### 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...
18. ### 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...
19. ### 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...
20. ### 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...
21. ### 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...
22. ### 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?
23. ### 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?
24. ### 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...