# Rigid bodies Definition and 30 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. ### A rotating rod acted upon by a perpendicular force

$$\tau = I\alpha$$ $$FL/2 = I\omega^2L/2$$ $$T = 1/\theta \sqrt{F/I}$$ would this be correct? I came up with this more basic question to solve a slightly harder question so I do not know the answer to the above-stated problem.
2. ### Reaction forces on a gyroscope

I know that ##\vec{v_c}=(\omega_1;-\omega_2;0)×(L;-r;0)=0## So ##\omega_2=\frac{r\omega_1}{L}## Then, using the system of coordinates shown in the picture and ##\Sigma M_z## I can find the reaction force in ##C##. But how can I find the reaction forces on ##A## and ##O##? I mean, what system...
3. ### Difference between curvilinear and rotational motion

The solution states that there's no rotational motion when ##C## is cut (the motion is curvilinear), so we can take torques with respect to the centre of mass of the plate. But, isn't it rotating? I think of it as a pendulum, which describes a circular motion. What's the difference? Wouldn't the...
4. ### Confusion About Rotational Motion

I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...
5. ### 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...
6. ### Calculating the Moment from a Different Vantage Point

Summary:: Just a simple 3d rigid dynamics question which I am trying to solve by placing coordinat system differently from original solution.Everything looks ok but results are different. Mod note: Post moved from technical section. Thats my question.As you see coordinate system was located...
7. ### Determine tensor of inertia of a rod

I have to find the inertia tensor of these rods and I don't have the concept that clear... I mean, I know the formulas like: ##I_{xx}=\int y^2 + z^2 dm## ##I_{xy}=\int xy dm## But I don't know what ##x, y, z, dm## stand for. In other words, I don't know what I should replace in the formula...
8. ### Rigid object in equilibrium

Here's the task: My attempt at a solution (I choose C as an axis): However, the textbook solution says D should be 58.8. What am I doing wrong?
9. ### Rotating Sphere: Conceptual Question

As shown in figure there's a homogeneous solid sphere. It is rotating about axis which is passing through point P directed perpendicular to the plane of paper. (In short like a pendulum). I'm neglecting gravity and assuming a force F which is directed perpendicular to the string. (The string...
10. ### 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...
11. ### A Euler's Principal Axis

When we solve Euler's differential equations for rigid bodies we find the angular acceleration ##\dot{\boldsymbol\omega}## and then the angular velocity ##\boldsymbol\omega##. Integrating ##\boldsymbol\omega## is less straightforward, so we start from a representation of the attitude, take its...
12. ### Rigid Bodies/ Angular Velocity

Homework Statement Homework Equations ##v=\omega r## The Attempt at a Solution So, using the equation, one can work out the velocity at point ##B##. ##v_B=\omega_{AB} \cdot r_B## ##v_B=6(0.4)=2.4~ ms^{-1}## I then tried working out the angular velocity at point ##C## using the...
13. ### Moment of Inertia of an Ammonium Molecule

Homework Statement The ammonium ion NH4+ has the shape of a regular tetrahedron. The Nitrogen atom (blue sphere) is at the center of the tetrahedron and the 4 Hydrogen atoms are located at the vertices at equal distances L from the center (about 1 Å). Denote the mass of the hydrogen atoms by Mh...
14. ### I Why is it T + f = Ma?

So I'm looking at a problem that involves a situation that looks like this the cylinder rolls without gliding. And there are these following equations that apply to it (1) mg - T = ma (for the block hanging vertically) (2) T + f = Ma (for the cylinder f = friction force, T = String force) (3)...
15. ### Rotation of Rigid Bodies: Rotating stick with disc on top

Homework Statement [/B] A thin cylindrical rod with the length of L = 24.0 cm and the mass m = 1.20 kg has a cylindrical disc attached to the other end as shown by the figure. The cylindrical disc has the radius R = 8.00 cm and the mass M 2.00 kg. The arrangement is originally straight up...
16. ### Instant centre of rotation

Homework Statement Homework Equations orthogonality condition: that means that the point of ICR is orthogonal to the velocity Vb and Va The Attempt at a Solution the solution that i found with the problem is: The ICR of the bar is at infinity. the motion of the bar is translational. I think...
17. ### Computing angular speed wrt CM I get a contradiction

Hello! I have been brushing up my Rigid Body Dynamics. I tried computing the angular speed with respect the Center of Mass (CM) using the usual split of kinetic energy and also the split of Angular momentum using the CM. First, a simple case: Two particles of mass M each separated by a distance...
18. G

### How can I find the length of this pole?

Homework Statement A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght. I'LL ATTACH AN IMAGE SO YOU CAN SEE IT. Homework Equations...
19. G

### How can I find the torque/moment of force about an axis?

Homework Statement The Trump's wall is so weak that has to be supported by two cables as is shown in the figure. If the tension over the cables BD and FE are 900 N and 675 N respectively. (I'LL UPLOAD AN IMAGE OF THE PROBLEM SO YOU CAN SEE IT) Homework Equations τ = r χ F Mo = r χ F The...
20. ### I Possible to estimate the location of a measurement point?

Hi guys, I am just wondering if it is possible to calculate/estimate the location of measurement point on a rigid body? For example, let's say we have a rigid body that is in motion. We attach a sensor, say an accelerometer on the surface of the rigid body. Now can we estimate the location of...
21. ### Finding the force of constraint--compound pendulum on spring

Homework Statement From Fetter and Walecka 5.1:[/B] Consider the compound pendulum in FIg 28.1 (mass M, moments of inertia Iij relative to the center of mass, which is a distance L from the point of support Q) but with Q attached to the bottom of a vertical spring (force constant k) and...
22. ### Torque on rigid body when angular momentum is not constant

I 'd like to clarify some doubts about the rotational motion around a fixed axis of a rigid body, in the case the angular momentum vector \vec {L} is not parallel to the angular velocity \vec {\omega} . In particular, consider a horizontal barbell with two equal masses m , forced to rotate...
23. ### Substituting spherical coordinates to evaluate an integral

I have to evaluate $$\int^1_{-1} \int^{ \sqrt {1-x^2}}_{ - \sqrt {1-x^2}} \int^1_{-\sqrt{x^2+y^2}}dzdydx$$ using spherical coordinates. This is what I have come up with $$\int^1_{0} \int^{ 2\pi}_0 \int^{3\pi/4}_{0}r^2\sin\theta d\phi d\theta dr$$ by a combination of sketching and...
24. ### Rolling without slipping over a plank

Homework Statement This is just a general case I'm having trouble trying to imagine: https://lh3.googleusercontent.com/-mTyOwzfLy0E/VluaNlxEddI/AAAAAAAAAEk/2Creguw3xzY/w530-h174-p-rw/Screenshot%2Bfrom%2B2015-11-29%2B21%253A34%253A50.png Suppose there is a cylinder, kind of like a yo-yo, that...
25. ### Predict the position of a particle on a rigid body

1. Problem Statement Assume there is an rigid object with mass m in 2D space, an impulse J = FΔt is applied at time t1 at the particle Pimp and Pimp is on the exterior boundary of the object. The impulse cause a free plane motion of the object and the object is only affected by the force of the...
26. ### Rotation of a rigid body about external axis

in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body - Rotation of a rigid body about a fixed axis is defined as...
27. ### Find the angular acceleration of the rod

Homework Statement Given: ##\mu_B=0.52## ##\theta=30^{\circ}## Weight- ##25## lb ##\omega=0## ## l=6## ft ##r_c=3\sqrt 2## radius of curvature. Homework Equations My Equations of motion are the following: ##\xleftarrow{+}\sum F_x=N_A\sin 60 - F_B=0## ##\downarrow{+} \sum F_y= N_A \cos...
28. ### Direction of friction acting on a rolling object

Hi! My question considers no specific problem, but rather different concepts I have trouble getting my head around. So I would be really happy if you could help me understand different kinds of friction, and maybe above all their direction, acting on a rolling object. :) Fist we have kinetic...
29. ### How to calculate velocities/forces from sphere collisions?

Hi, Basically I have a point cloud that represents balls with different radii. They are all moving based on forces and sometimes they are intersecting with each other. Imagine the yellow ball is going in one direction while the blue balls goes in another direction. At one time they are...
30. ### Finding angle required for equilibrium on a slope

Homework Statement A heavy uniform cylindrical drum is placed, with its axis horizontal, on a slope inclined at an angle α to the horizontal. It is prevented from sliding or rolling down the slope by a triangular wedge. The weight of the wedge is negligible compared with the weight of the drum...