What is Rigid bodies: Definition and 127 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).
The questions and relevant formulas/information are attached below:
I started by writing the needed values:
2 kN = 2,000 N
6378 km =6378(1000) m
1800 km = 1800(1000)m
After converting, I tried solving for the mass using the law of gravitation formula:
I decided to replace N as...
The problem is from Hibeller's book, Mechanics: Statics and attached below is the picture of the problem:
My question about this problem is about the FBD of the reactions. Here is how I drew it:
But when I tried checking the solution for the problem, they have this as their FBD:
My...
Consider the above setup. Here, to get the kinetic energy of the body, the moment of inertia with respect to the ##y-##axis has to be calculated. This can be done in two ways:
1. The moment of inertia of the rotation around the center of mass is ##\Theta_s##, then the kinetic energy is...
Ok. So, I already worked on this problem, and get ##m_c## = 2m/3, which is correct according to the book.
However, I also want to know the value of the tension (T) between rod A and B.
Note: Before we start working on my modified question, I want to point out that the force exerted by the...
I'm trying to understand basic principles of ancient thrown weaponry. Let's say we have something like a bar with a known inertia tensor that is thrown from one end such that it is both rotating and translating. If it strikes something along either side of its center of mass (an off-center...
The boom is supported by a ball-and-socket joint at AA and a guy wire at BB
Hey guys, I am stuck with this question in find the Tension in B and the moments around A. I have done plenty of 2d Tension questions but not a 3D one.
$$\tau = I\alpha$$
$$FL/2 = I\omega^2L/2$$
$$T = 1/\theta \sqrt{F/I}$$
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.
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...
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...
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...
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...
This post is also an invitation to compose problems of the presented below type.
The Lagrange–d'Alembert principle by itself is used very seldom. It is usually used to derive the Lagrange equations and that is all. But actually it is a powerful tool in nonholonomic mechanics.
As an example...
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...
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...
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...
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...
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...
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 instantaneous...
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...
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)...
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...
Homework Statement
Two uniform 150 N rafters rest on frictionless floor, held together by a rope. A 500 N load is held at their apex. Find tension in the tie rope.
Homework Equations
##torque= rFsin \theta =Force*Moment Arm ##
The Attempt at a Solution
The angle ##\theta## in the picture...
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...
I set a small project for myself to design a controller for a rocket, which moves a mass around to shift the center of mass, in order to steer a rocket.
The picture shows a simplified model of a rocket plus a movable mass. , shown is a rod for the rocket, and a mass for the controller. there...
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...
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...
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...
Okay...I have a simple question that, if we apply a force to a wall, then according to F=ma, the wall should have some acceleration at all the points we are applying the force...My question is that since the wall does not move move back, does this acceleration only result in a slight deformation...
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...
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...
Homework Statement
Homework EquationsThe Attempt at a Solution
When the barrel starts to tip, the normal at point A should be 0 Newtons, and then all weight would be on point B.
I'm guessing if the barrel would tip, it wouldn't be sliding across the floor so kinetic friction is not used...
Homework Statement
A block and spool are each pulled by a string across a frictionless surface. The string is wound around the spool such that it may unwind as it is pulled, the string attached to the block is at the center of mass. The block and spool have the same mass and the strings...
I saw this problem in my dynamics class: http://d2vlcm61l7u1fs.cloudfront.net/media%2Fa22%2Fa2261e7a-0e85-45e7-8b63-f23157d623bc%2Fphp37ql1a.png
I know how to solve it, but I don't understand why A(bd) has both a normal and tangential component to acceleration. If it is rotating at a 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...
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...
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...
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...
Homework Statement
1.
It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large...
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...
Homework Statement
why 2/3 is required in this calculation as circled ? I have no idea.
I know that 4.5/2 is the distance of the centroid of the bar from point A .
Homework EquationsThe Attempt at a Solution
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...
Homework Statement
http://tinypic.com/r/vsew5k/8
Homework Equations
Angular momentum for rigid bodies
Kinetic energy of rigid bodies
The Attempt at a Solution
I tried to start by using conservation of energy, but I can't find the center of mass of the rod. I'm also not sure where to put the...
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...
Consider a partially filled bottle of water. When it's tipped over and rotating about its pivot point where its edge touches the ground, it has an angular acceleration. Assuming the liquid is not viscous at all, so flows perfectly, at a given instant can it be considered to have a moment of...
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...
Suppose I have some sort of rigid body, a solid sphere let's say. For simplicity's sake let's assume that the sphere can only rotate about a single arbitrary axis through the center of mass. If the center of mass of the sphere is traveling with a constant velocity (with respect to some arbitrary...