Angular momentum, law of conservation of angular momentum, elastic collision are defined and explained. This video is ed by the jeff hanson for the private use of our audience. Dynamics and control challenges that occurred during the apollo project courtesy of dr. Chapter 11 dynamics of rigid bodies university of rochester. Description the lecture note deals with the dynamics of rigid bodies. Universi dynamics of particle and rigid bodies by chakroborty and ghoshu. There are two types of motion involved in the case of rigid body viz the translation and the rotation. Plane kinematics of rigid bodies relative motion analysis.
The trajectory of any point in the body, used as reference point, gives the variation of three of these degrees of freedom. Kinematics and dynamics of particles and rigid bodies in plane. 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. This chapter shows us how to include rotation into the dynamics. Many of the equations for the mechanics of rotating objects are similar to the motion equations for linear motion. Since you have a direction and a magnitude, you might suspect that rotations could be represented in some way by vectors. So far, we have only considered translational motion. For twodimensional rigid body dynamics problems, the body experiences motion in one plane, due to forces acting in that plane.
Rotational motions of a rigid body mechanics physics. Pdf, we environment in fact distinct that this baby book can be a fine material to read. Its eigenvectors are special directions within the rigid body called the principal axes. The hammer in the figure is placed over a block of wood of 40 mm of thickness, to facilitate the extraction of the nail. Use the given information to nd the position function of the particle. Kinematics of rigid bodies islamic university of gaza. Branches of dynamics dynamics is divided into two branches called kinematics and kinetics. Objects deform elastically, but these deformation are negligible for. The angular velocity of oa is the same as that of the wheel. Common areas for discussion include accessibility of pdf files, images. This is an article on the basics of motion in rigid bodies. In this section we will study the kinematics of a rigid body, i.
Rigid bodies which are fixedpivoted experience motion which is rotational. General form of plane motion motion of each point in the body, e. General motion motion about a fixed point general plane motion rotation about a fixed axis curvilinear translation rectilinear translation. 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. The vector sum v a can be calculated from law of cosines. Rectilinear motion, curvilinear motion rectangular, normal tangential, polar, cylindrical, spherical coordinates, relative and constrained motion, space curvilinear motion. Spinning objects like tops, wheels, and the earth are all examples of rotational motion that we would like to understand. Curvilinear motion of a point a is related to the angular motion of the rigid body by the familiar nt coordinate kinematic relationship. A car is driven along a straight track with position given by st 150t 300 ft t in seconds. Investigates kinematics principles for analyzing rectilinear and curvilinear motion of. Many of the equations for the mechanics of rotating objects are similar to the motion equations. Introduction to kinematics of rigid bodies kinematics of rigid bodies. Energy and momentum methods for plane motion of rigid bodies pdf. This term is used to define the motion of a particle or body without consideration of the forces causing the motion.
Given any external forces acting on a rigid body, well show how to simulate the motion of the body in response to these forces. A body is said to undergo planar motion when all parts of the body move along paths equidistant from a fixed plane. 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. As we shall see, these can often be counterintuitive. Then, the time derivatives of the relations are done to obtain velocities and accelerations. Computer programs or procedures can be written that simulate many of these realworld dynamics. A general rigid body subjected to arbitrary forces in two dimensions is shown below. Kinetics is the branch of mechanics that relates the force acting. Planemotion equations again unconstrained and constrained motion systems of interconnected bodies stepbystep solution process rigidbody translation. The systems we will consider are the spinning motions of extended objects. We are given that st 150t 300 ft, so vt st 150 fts, and at vt 0 fts2. Here we will consider dynamics, which deals with the accelerated motion of a body.
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. 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. Rotational motion of a rigid body notes rigid body dynamics. File type pdf engineering mechanics dynamics amp part i rectilinear motion solved university problems this ezed video explains. Definition of center of mass for two particle system and rigid body is given. 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. 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.
Motion we observe in the realworld can often be described or simulated mathematically. Kinematics and dynamics of particles and rigid bodies in plane motion study notes. In this chapter we will consider the motion of solid objects under the application of forces and torques. R is the angular ve locity of reference frame r in reference frame f. Having now mastered the technique of lagrangians, this section will be one big application of the methods. The translational motion of a rigid body in space was treated in part ii. 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. Maximum compression of a spring attached to a mass and colliding with another body is calculated.
Thankfully, this problem is identical to that of an object xed at a point. It starts with the geometric relations that define the configuration involved. Consider a ball bouncing and colliding with other objects, spinning tops, shattering a window. Kinematicsthe study of a bodys motion independent of the forces on the body. Equation of motion for two particle system is derived. 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. Dynamics is the branch of mechanics which deals with the study of bodies in motion. Kinematics concerned with the geometric aspects of motion 2. 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.
Well concentrate on rotation of rigid bodies, so keep in mind that what we say does does not apply to jellyfish. Rotation of a rigid body not all motion can be described as that of a particle. 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. Rectilinear motion using integration solutions to selected. Rotation of a rigid body in rigid body dynamics we have two types of motion. Kinematics of rigid bodies relations between time and the positions, velocities, and accelerations of the particles forming a rigid body. Note that displacement is not the same as total distance. Pdf particle dynamics, material system dynamics and rigidbody. Direction of relative velocity is perpendicular to oa. Use kinematics to solve rigid body mechanics for forces, velocities, and accelerations. Kinetics concerned with the forces causing the motion mechanics. Wolfgang pauli and niels bohr stare in wonder at a spinning top. The simulation of realworld motion is a branch of physics called dynamics. Rectilinear motion using integration solutions to selected problems calculus 9thedition anton, bivens, davis matthew staley november 15, 2011.
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. 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. 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. Particles have mass but negligible size and have only 3 translational degrees of freedom. However we are often interested in the rotation of a free body suspended in space for example, a satellite or the planets. Rigid body mechanics me101 statics dynamics deformable body mechanics, and fluid mechanics. For example, an airplane has 6 degrees of freedom i. 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. 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. 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. Rotational motion is more complicated than linear motion, and only the motion of rigid bodies will be considered here.