General motion motion about a fixed point general plane motion rotation about a fixed axis curvilinear translation rectilinear translation. Pdf, we environment in fact distinct that this baby book can be a fine material to read. The translational motion of a rigid body in space was treated in part ii. Rigid bodies which are fixedpivoted experience motion which is rotational. Equation of motion for two particle system is derived. Direction of relative velocity is perpendicular to oa. Maximum compression of a spring attached to a mass and colliding with another body is calculated. Rectilinear translation parallel straight paths curvilinear translation rotation about a fixed axis curvilinear translation rotation 1 2 3 plane motion v, a 0 parallel circles concentric circles. Consider a ball bouncing and colliding with other objects, spinning tops, shattering a window.
The angular velocity of oa is the same as that of the wheel. Chapter 1 rigid body dynamics in order to describe the attitude of a rigid body and to determine its evolution as a function of its initial angular velocity and applied torques, eulers angles and eulers equations of motion need to be introduced. Universi dynamics of particle and rigid bodies by chakroborty and ghoshu. Rotational motions of a rigid body mechanics physics. A car is driven along a straight track with position given by st 150t 300 ft t in seconds. We are given that st 150t 300 ft, so vt st 150 fts, and at vt 0 fts2.
Rigidbody dynamics the motion of a rigid body in space consists of the translational motion of its center of mass and the rotational motion of the body about its center of mass. Mg is the sum of the moments about an axis passing through the center of mass g in the zdirection, pointing out of the page. Rectilinear motion, curvilinear motion rectangular, normal tangential, polar, cylindrical, spherical coordinates, relative and constrained motion, space curvilinear motion. Curvilinear motion of a point a is related to the angular motion of the rigid body by the familiar nt coordinate kinematic relationship. Motion we observe in the realworld can often be described or simulated mathematically. The dynamics of a rigid body has been discussed in our introductory courses, and the techniques discussed in these courses allow us to solve many problems in which. In this chapter we define a rigid body and describe how the number of degrees of freedom of a rigid body with n particles is determined. Dynamics is the branch of mechanics which deals with the study of bodies in motion. Pdf particle dynamics, material system dynamics and rigidbody. Kinematics and dynamics of particles and rigid bodies in plane motion study notes.
Having now mastered the technique of lagrangians, this section will be one big application of the methods. Kinematics and dynamics of particles and rigid bodies in plane. So far, we have only considered translational motion. Angular momentum, law of conservation of angular momentum, elastic collision are defined and explained. Its eigenvectors are special directions within the rigid body called the principal axes. A body is said to undergo planar motion when all parts of the body move along paths equidistant from a fixed plane. Definition of center of mass for two particle system and rigid body is given. This chapter shows us how to include rotation into the dynamics. Well concentrate on rotation of rigid bodies, so keep in mind that what we say does does not apply to jellyfish. It starts with the geometric relations that define the configuration involved. Our approach will be to consider rigid bodies as made of large numbers of particles and to use the results of chapter 14 for the motion of systems of particles. Chapter 11 dynamics of rigid bodies a rigid body is a collection of particles with fixed relative positions, independent of the motion carried out by the body. Planemotion equations again unconstrained and constrained motion systems of interconnected bodies stepbystep solution process rigidbody translation. File type pdf engineering mechanics dynamics amp part i rectilinear motion solved university problems this ezed video explains.
This term is used to define the motion of a particle or body without consideration of the forces causing the motion. Rectilinear motion using integration solutions to selected problems calculus 9thedition anton, bivens, davis matthew staley november 15, 2011. Spinning objects like tops, wheels, and the earth are all examples of rotational motion that we would like to understand. Description the lecture note deals with the dynamics of rigid bodies. Given any external forces acting on a rigid body, well show how to simulate the motion of the body in response to these forces. Motion of rigid bodies under external forces and torques the general motion of a rigid body can be decomposed into a linear motion of a point mass equal to that of the body located at the center of mass of the body under an external force and a rotational motion about the center of mass under.
Then, the time derivatives of the relations are done to obtain velocities and accelerations. This video is ed by the jeff hanson for the private use of our audience. Rigid body motion in this chapter we develop the dynamics of a rigid body, one in which all interparticle distances are xed by internal forces of constraint. Use kinematics to solve rigid body mechanics for forces, velocities, and accelerations. Kinetics is the branch of mechanics that relates the force acting. This is, of course, an idealization which ignores elastic and plastic deformations to which any real body is susceptible, but it is an excellent approximation for. The trajectory of any point in the body, used as reference point, gives the variation of three of these degrees of freedom. Note that displacement is not the same as total distance. Rotational motion of a rigid body notes rigid body dynamics. The dynamics of the rigid body consists of the study of the effects of external forces and couples on the variation of its six degrees of freedom.
Objects deform elastically, but these deformation are negligible for. In this chapter we will consider the motion of solid objects under the application of forces and torques. Chapter 11 dynamics of rigid bodies university of rochester. However we are often interested in the rotation of a free body suspended in space for example, a satellite or the planets.
Use the given information to nd the position function of the particle. This is an article on the basics of motion in rigid bodies. Kinematics of rigid bodies relations between time and the positions, velocities, and accelerations of the particles forming a rigid body. If a force of 200 n perpendicular to the hammer is required to extract the nail, find the force on the nail and the force at. The vector sum v a can be calculated from law of cosines. Rotation of a rigid body not all motion can be described as that of a particle. For twodimensional rigid body dynamics problems, the body experiences motion in one plane, due to forces acting in that plane.
Plane kinematics of rigid bodies relative motion analysis. General form of plane motion motion of each point in the body, e. As we shall see, these can often be counterintuitive. Kinematics of rigid bodies islamic university of gaza. Many of the equations for the mechanics of rotating objects are similar to the motion equations for linear motion. A rigid body is an object with a mass that holds a rigid shape, such as a phonograph turntable, in contrast to the sun, which is a ball of gas.
Common areas for discussion include accessibility of pdf files, images. Rotation of a rigid body in rigid body dynamics we have two types of motion. Rigid body mechanics me101 statics dynamics deformable body mechanics, and fluid mechanics. Branches of dynamics dynamics is divided into two branches called kinematics and kinetics. Investigates kinematics principles for analyzing rectilinear and curvilinear motion of. Kinetics concerned with the forces causing the motion mechanics. The systems we will consider are the spinning motions of extended objects. Introduction to kinematics of rigid bodies kinematics of rigid bodies. Kinematics concerned with the geometric aspects of motion 2. Linear motion also called rectilinear motion is a onedimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. Dynamics and control challenges that occurred during the apollo project courtesy of dr.
There are two types of motion involved in the case of rigid body viz the translation and the rotation. Many of the equations for the mechanics of rotating objects are similar to the motion equations. For example, an airplane has 6 degrees of freedom i. The hammer in the figure is placed over a block of wood of 40 mm of thickness, to facilitate the extraction of the nail. Computer programs or procedures can be written that simulate many of these realworld dynamics. Rigidbody dynamics below are selected topics from rigidbody dynamics, a subtopic of classical mechanics involving the use of newtons laws of motion to solve for the motion of rigid bodies moving in 1d, 2d, or 3d space.
A general rigid body subjected to arbitrary forces in two dimensions is shown below. Thankfully, this problem is identical to that of an object xed at a point. Rectilinear motion using integration solutions to selected. R is the angular ve locity of reference frame r in reference frame f. The motion of a rigid body which is not fixed or pivoted is either a pure translational motion or a combination of translational and rotational motion. Rotational motion is more complicated than linear motion, and only the motion of rigid bodies will be considered here. In other words, the rolling motion of a rigid body can be described as a translation of the center of mass with kinetic energy kcm. Lecture notes dynamics aeronautics and astronautics. Energy and momentum methods for plane motion of rigid bodies pdf. The simulation of realworld motion is a branch of physics called dynamics. Kinematicsthe study of a bodys motion independent of the forces on the body. Since you have a direction and a magnitude, you might suspect that rotations could be represented in some way by vectors. In this section we will study the kinematics of a rigid body, i.
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