Rigid body Definition and 356 Threads

Homework Statement A solid body consisting in two concentric disks of masses m1, m2 and radius r1<r2 is linked through a ideal rope to a mass m which falls down with a certain acceleration. The solid body moves of pure rolling. Find the acceleration a of the mass. Homework Equations P-T=m*a...

I am trying to solve problem number 4 part A and B from (http://people.physics.tamu.edu/kamon/teaching/phys218/exam/2003C/2003C_Exam3_Solution.pdf) but I am confused about certain aspects of it. In part A, I understand that since we are considering the person as a cylinder, the equation for...

Let's say I have a ball 299792458m away and i want to apply a force to it. Evidently any information (for eg if i instantaneously increase my mass to increase the gravitational force) will travel at the speed of light and thus, the increase in gravitational force will only be felt by the ball 1...

Hi folks, This week I have a question about rigid body dynamics analyses in CAE. This is in relation to the final year project of my degree. Over the past few months I've been working with AnSys 18.1 for FEA however, I've reserved AnSys exclusively for static analyses. For rigid body dynamics...

Homework Statement In the figure there are a block 1 of mass ##M##, a pulley (disk) of mass ##M## and radius ##R## and a second block of mass ##2M## on an inclined plane with an angle ##\alpha## with respect to the horizontal. On this plane the static friction is ##\mu##. The wire does NOT slip...

Homework Statement this has been bugging me for a while now the angular momentum about any point p is given as ## \vec {L_p} = \vec {R_{cm,p}} \times \vec {P_{cm}} + L_{cm}\\ ## now if the body precessing around z axis and spinning about its own axis then angular velocity of body in lab...

Just to confirm a few points: A body frame rotates with a body. It need not be aligned to the rotation axis. Angular momentum vector always aligned with rotation axis (not deviates from it). An observer on the body surface (body frame) observes no motion on a body. Principal axis of rotation...

What does it mean where it says it provides couples on x-axis and z axis? Anyways what am I doing wrong? my procedure is finding tension in cables by summing moments about point A. then with the tensions, finding reactions at A. However when i sum the moments about A I get 3 equations 2...

Homework Statement Rigid body (ship) rotate and moves around 3 axis (x,y,z) around the center of gravity. The position is of the center of gravity is not known. What is known: At a point (A) the accereleration, velocity and position and rotational acceleration, velocity and position are known...

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...

Homework Statement A) Use Euler's equations to solve for the precession rate of a rapidly spinning gyroscope precessing uniformly (no nutation). Use I3 for the moment along the z axis along the axle. Beginning with Euler's equations, derive the coupled equations: ## \dot ω_1 + Ω ω_2 = \frac...

Hello all, First of all I want to mention what believe or result of concepts, do I hold about rotational motion especially about the angular velocity. I assume that unlike velocity angular velocity has to worked out from some point. I will begin with particle for this I assume that the question...

Question: A) Derive the work - energy theorem for one particle. B) Check whether it is applicable for a system of particles and a rigid bodyWork - energy theorem for one particle system, total sum of work done by individual forces = work done by total force To show the above equality, let's...

Homework Statement Two masses of 2 kg are attached to the extremities of a 5 cm long, negligible mass and thin bar, free to rotate around a horizontal axis passing through its center. A drop of wax falls on one of the two masses at ##v = 3 \frac{m}{s}## and sticks to it. Retrieve the angular...

hi guys, i am new user on ansys i have task from my lecturer. it is about static test for seat bus. i try simulate the seat bus on ansys statical structural. you can see my model on attachment (untitle1.png). at that picture, there are 2 bars will push the seat back. the stiffness beahvior of...

Hi. I am revising my Mechanics: Dynamics by reading the Beer 10th edition textbook and Pytel 2nd edition In Pytel pg 358 art. 17.3 the angular momentum about the mass center of a rigid body in general motion is being calculated...

Homework Statement We place a cylinder with radius R, a sphere with radius R and a sphere with radius (2R). Which of the solids will roll out of the plane first? Assume no rolling resistance and no air resistance. Homework Equations 1) The net torque is the torque of the force of static...

I am wondering, when solving rigid body exercises, how can I express the relationship between linear and angular acceleration for a general case? E.g. what would be the linear acceleration in function of the angular one of a 1m rod that is rotating through a fixed point 0.6 m away from its mass...

Consider a circle rotating about a point X on its circumference at ##\omega = 2## rad/s. That means all points on and in the circle rotate at the same ##\omega = 2## rad/s. What are the angular velocities of various different points, say points A, B and C, with respect to the centre O of the...

Hello, Homework Statement I'm given the following exercise: "A rod with neglected thickness exists. What is the relation between the α,β angles to Euler angles of orientation? α is defined as the angle between the rod and its projection on the XY plane. β is defined as the angle between the...

Homework Statement Determine the moment of inertia of a rigid body on the picture: The radius of the inner cylinder is R and the outer is 2R. Homework Equations 3. The Attempt at a Solution [/B] I thought of subtracting the big cylinder inertia from the small and adding the hanging body and...

1. The problem statement, all variables and given/known See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis Homework Equations I=mr^2 The Attempt at a Solution I tried to get the moment of intertia of rod by integration from...

Suppose we have a rigid body that rotates around a point P other than its center of mass, with point P being a point of the rigid body. This implies that there are external forces to the rigid body. If the external forces cease to exist(like we have an axis passing through P and we suddenly...

Homework Statement In the mechanism shown below, the angular velocity of link 2 is 17 rad/s CW, constant. Find the angular velocity (magnitude and direction) of link 3. The distance between A and C is 109 mm, the length of link 3 is 125 mm, and θ= 111°. Note: B is a pin-slider In the...

a disc of mass m and radius r rolls down a slope of incline tan^-1 3/4. the slope is rough enough to prevent slipping. the disc travels from rest a distance of s metres straight down the slope. (i) show that the linear acceleration of the disc is 2/5 g. what i did was i first revolved the forces...

Homework Statement The wheel shown rotates about point O. Point A has a velocity=-7j in/sec. Point B has a tangential velocity=-4i in/sec^2 Determine the absolute acceleration of Point C located on the circle. radius=6 in You will have to look at the figure for more clarification please...

Homework Statement Attached is a pdf of the assignment problems, I'm looking at problem 1 under the "Try" section. It shows a rod attached to a wall bracket on the left, with a force applied on the right side. I'm also including a link to the solution, it's under "Problem 3.83" -...

I'm confused about this rolling without (or better with) slipping situation. Suppose to have a disk with initial velocity ##v## and angular velocity ##\omega##. The motion is to the right but the angular velocity is counterclockwise. There are no forces acting on the disk besides the kinetic...

Homework Statement A rigid body is made of three identical thin rods, each with length L = 0.530 m, fastened together in the form of a letter H, as suggested by the figure here. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body...

in rigid body dynamics is this relation between velocity of centre of mas and velocity of any particle in the rigid body correct? vcm = vp + rXω r is the position vector of the particle with respect to centre of mass relations are written in vector form and also tell me how to calculate...

Homework Statement A disc of mass M and radius r is kept on a horizontal,frictional plane and is connected to a horizontal spring at the centre.A particle of mass m strikes the topmost point of the disc,tangentially and sticks to it.Assume that the mass of the particle is m and it's velocity is...

For the rotation of a rigid body about a fixed axis z the following holds. $$\vec{\tau_z}=\frac{d\vec{L_z}}{dt}= I_z \vec{\alpha} \tag{1}$$ Where \vec{\tau_z} is the component parallel to the axis z of a torque \vec{\tau} exerted in the body; \vec{L_z} is the component parallel to the rotation...

Consider the rotation of a rigid body about a fixed axis z, not passing through a principal axis of inertia of the body. The angular momentum \vec{L} has a parallel component to the z axis (called \vec{L_z}) and a component perpendicular to it (called \vec{L_n}). I have some doubts on...

Homework Statement A disk roll without slipping down a incline plane. Identify the forces acting on the disk, explain qualitatively which of these forces do work. Homework Equations The rotational work is given by W=\int \tau_z d\theta (1) , where \tau_z is the component of the torque...

Homework Statement [/B] Consider a barbell with two equal masses m that rotates around a vertical axis z not passing through its center with angular velocity \vec{\omega}. The barbell is forced to stay in this position by an appropriate support. Identify the forces exerting torques on the...

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...

Homework Statement A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disc of mass ‘M’ and radius ‘R’ (<L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its centre and (case B) the...

When we looked at some closed surface, we defined the overall electric flux of that surface as the sum of all infinitesimal fluxes of all the infinitesimal surfaces that make the quoted closed surface. Does that change if we do not have a closed surface, but a rigid body such as, let's say, a...

Mentor note: moved to homework forum later, therefore no template. When doing a rigid body relative motion (accel) problem using vector analysis, how do I know when it's appropriate to substitute sin/cos values vs when to use just the numbers given as the velocity?

Homework Statement A rod attached to a ceiling at one end and a disc on the other end is performing SHM. In case (1) the disc cannot rotate. In case (2) the disc can rotate about its centre. Compare the restoring torque and angular frequency in both cases. Homework Equations...

Homework Statement What will be the speed of sound in a perfectly rigid body? Given : In a hypothetical situation we have a rigid body find the speed of sound when it passes through the material. Elasticity of medium = ∞ Homework Equations velocity = √E/ρ ρ = density E = elasticity of medium...

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 Consider an arbitrary rigid body with an axis of rotational symmetry, which we'll call ## \hat z ## a.) Prove that the axis of symmetry is a principal axis. (b) Prove that any two directions ##\hat x## and ##\hat y ## perpendicular to ##\hat z ## and each other are also...

Hi, I am having some problems conceptualizing the Euler's Theorem. Any help will be greatly appreciated. In Goldstein's book the Euler's theorem is stated as 'Any displacement of a rigid body, whose one point remains fixed throughout, is a rotation about some axis', then he has proven that the...

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 Given the following diagram If the crate produces a force of gravity of 491 N from the center of gravity G, determine the normal force on both of the wheels and the magnitude and direction of the minimum force required at the grip B needed to lift the load. Homework...

Hi everyone, I was recently talking to someone with a non-maths background about rotational stability, in particular how rotation is stable around the largest and smallest principal moments but not the intermediate one. He asked me if there was any 'obvious' reason for this, but one didn't...

1. The problem statement, all variables and given/know Say I have a can of water, and I am rotating it about its central axis at a constant angular rate. The water in the tank should make a 3D almost parabolic curve as it touches the the walls of the tank. Can I use Bernoulli's equation along...

Hi, I have a question about rigid body rotation. If I have a rod out in space in free float and I attach a battery powered fan to center of mass and then the fan is turned on to spin in a clockwise direction, then the rod should spin in a counterclockwise direction. This much I...