Uniform Rectilinear Motion

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1 Engineeing Mechanics : Dynamics Unifom Rectilinea Motion Fo paticle in unifom ectilinea motion, the acceleation is zeo and the elocity is constant. d d t constant t t 11-1

2 Engineeing Mechanics : Dynamics Unifomly cceleated Rectilinea Motion Fo paticle in unifomly acceleated ectilinea motion, the acceleation of the paticle is constant. d a constant d a at t at d t at d t 1 at ( at) t 1 at d d a constant d a d a ( ) 1 ( ) a( ) 11 -

3 Engineeing Mechanics : Dynamics Motion of Seeal Paticles: Relatie Motion Fo paticles moing along the same line, time should be ecoded fom the same stating instant and displacements should be measued fom the same oigin in the same diection. elatie position of with espect to elatie elocity of with espect to a a a a a a elatie acceleation of with espect to 11-3

4 Engineeing Mechanics : Dynamics Motion of Seeal Paticles: Dependent Motion Position of a paticle may depend on position of one o moe othe paticles. Position of block depends on position of block. Since ope is of constant length, it follows that sum of lengths of segments must be constant. constant (one degee of feedom) Positions of thee blocks ae dependent. constant (two degees of feedom) C Fo linealy elated positions, simila elations hold between elocities and acceleations. d d d d d d C C o o a a C a C 11-4

5 Engineeing Mechanics : Dynamics Cuilinea Motion: Position, Velocity & cceleation Conside paticle which occupies position P defined by at time t and P defined by at t t, d lim t t instantaneous elocity (ecto) lim t s ds t instantaneous speed (scala) 11-5

6 Engineeing Mechanics : Dynamics Cuilinea Motion: Position, Velocity & cceleation Conside elocity of paticle at time t and elocity at t t, d a lim t t instantaneous acceleation (ecto) In geneal, acceleation ecto is not tangent to paticle path and elocity ecto. 11-6

7 Engineeing Mechanics : Dynamics Rectangula Components of Velocity & cceleation When position ecto of paticle P is gien by its ectangula components, i y j zk Velocity ecto, d dy dz i j k i j k y z i & y & j zk & cceleation ecto, d d y d z a i j k a i a j a k y z && i && y j && zk 11-7

8 Engineeing Mechanics : Dynamics Rectangula Components of Velocity & cceleation Rectangula components paticulaly effectie when component acceleations can be integated independently, e.g., motion of a pojectile, a && a && y g a & z with initial conditions, y z y ( ), ( ),( ) y z Integating twice yields ( ) ( ) y y gt z 1 ( ) t y ( ) t gt z y Motion in hoizontal diection is unifom. Motion in etical diection is unifomly acceleated. Motion of pojectile could be eplaced by two independent ectilinea motions. z 11-8

9 Engineeing Mechanics : Dynamics Motion Relatie to a Fame in Tanslation Designate one fame as the fied fame of efeence. ll othe fames not igidly attached to the fied efeence fame ae moing fames of efeence. Position ectos fo paticles and with espect to the fied fame of efeence Oyz ae and. Vecto joining and defines the position of with espect to the moing fame y z and Diffeentiating twice, elocity of elatie to. a a a a acceleation of elatie to. bsolute motion of can be obtained by combining motion of with elatie motion of with espect to moing efeence fame attached to. 11-9

10 Engineeing Mechanics : Dynamics Tangential and Nomal Components a d d et en at an ρ ρ Tangential component of acceleation eflects change of speed and nomal component eflects change of diection. Tangential component may be positie o negatie. Nomal component always points towad cente of path cuatue. 11-1

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