chapter12(2)

# chapter12(2) - Ch. 2: Kinematics of Particles 2.0 Outline...

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Ch. 2: Kinematics of Particles 2.0 Outline ± Introduction ± Rectilinear Motion ± Plane Curvilinear Motion ± Rectangular Coordinates (x-y) ± Normal and Tangential Coordinates (n-t) ± Polar Coordinates (r- θ ) ± Relative Motion (Translating Axes) 2.0 Outline

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Ch. 2: Kinematics of Particles 2.1 Introduction 2.1 Introduction Kinematics is the study of the motion of bodies with no consideration to the forces that accompany the motion. It is an absolute prerequisite to kinetics, which is the study of the relationships between the motion and the corresponding forces that cause the motion or are generated as a result of the motion. A particle is a body whose physical dimensions are so small compared with the radius of curvature of its path. This makes the body rotation effect insignificant and the motion of the body can be treated as that of the particle.
Ch. 2: Kinematics of Particles 2.1 Introduction Position of P rectangular coordinates x, y, z cylindrical coordinates r, θ , z spherical coordinates R, θ , Φ Motion of P absolute motion analysis relative motion analysis Absolute motion analysis: coordinates measured from fixed reference axes, e.g. motion of the piston described by the frame fixed to the ground Relative motion analysis: coordinates measured from moving reference axes, e.g. motion of the piston described by the frame attached to the car

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Ch. 2: Kinematics of Particles 2.2 Rectilinear Motion: motion along a straight line 2.2 Rectilinear Motion () av t0 If change in the position coordinate during t is the displacement s , v s/ t ds 1 __ instantaneous velocity, v lim s/ t s dt velocity time rate of change of the position coord., s If change in th Δ→ Δ Δ± = Δ Δ Δ = = = ± av 2 2 e velocity during t is v, a v/ t dv d s 2 __ instantaneous acceleration, a lim v/ t v s dt dt 3 __ vdv ads ΔΔ = Δ Δ = = = = = = ±± ±
Ch. 2: Kinematics of Particles 2.2 Rectilinear Motion Displacement vs. Distance displacement: vector quantity involving initial and ending position distance: positive scalar quantity Both velocity and acceleration are vector quantities Æ generally their changes include 1) change in magnitude and 2) change in direction For rectilinear motion, direction is the constant straight line path Æ algebraic problem Integration of basic differential relations

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Ch. 2: Kinematics of Particles 2.2 Rectilinear Motion () 22 11 st 21 vt vs ds vdt, s s area under v-t curve dv adt, v v area under a-t curve vdv ads, v v / 2 area under a-s curve =− = = = ∫∫ Relationships among several motion quantities graphic/numerical vs. algebraic approach
Ch. 2: Kinematics of Particles 2.2 Rectilinear Motion () dd kinetic relation dt dt dt dt s v a v, s, t F v, s, t ∫∫ RR common problems: know a, find s by integration

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Ch. 2: Kinematics of Particles 2.2 Rectilinear Motion () o oo o vt o v0 vs 22 st t 2 o s0 0 at the beginning, t 0, s s , v v at time t, dv a dt v v at vdv a ds v v 2a s s ds vdt v at dt s s v t at / 2 = == =→ = + = + ==+ = + + ∫∫ a) a = constant, e.g. G-force, dry friction force
Ch. 2: Kinematics of Particles 2.2 Rectilinear Motion () () () o o vt t o v0 0 st t t t oo o s0 0 0 0 o dv f t dt v v f t dt

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## This note was uploaded on 05/07/2011 for the course 3ME WB1114 taught by Professor I.paraschiv during the Spring '08 term at Technische Universiteit Delft.

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chapter12(2) - Ch. 2: Kinematics of Particles 2.0 Outline...

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