Electrical - MECH 2 Dynamics Formula and Data Sheet Some Standard Physical Constants Acceleration at Sea Level due to Gravity g = 9.81 m/s 2 Speed

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MECH 2 Dynamics Formula and Data Sheet Some Standard Physical Constants: Acceleration at Sea Level due to Gravity: 2 m/s 81 . 9 = g . Speed of light: m/s 10 3 8 × = c . (Nothing in this course goes that fast, so please check your work if you compute a number anywhere near this!) Particle Kinematics-(Phys 170 Review Material) Concept Formulae Rectilinear (Straight Line) Motion: This occurs when position, velocity and acceleration are all along the same direction. v ds dt a dv dt ads vdv == = for constant acceleration: () sa t v t s va tv vv a s s c c c =+ + 1 2 2 2 00 0 2 0 2 0 Curvilinear (curved-path) motion can be described using: Rectangular components ( fixed frame of reference). Normal and tangential components ( instantaneous frame of reference with respect to the path ). The tangential component, u t , is along the path of the particle at the particular instant in time. The normal component, u n , is perpendicular to the tangential component and points toward the centre of curvature of the path at that point. The binormal component, u b = u t x u n . Cylindrical (including polar) coordinates ( instantaneous frame of reference, with respect to a fixed origin ). The radial component, u r is along the vector from the origin to the particle. The transverse component, u θ is along the direction of increasing angle θ with respect to a fixed reference line. The third component direction is along the z axis out of the plane of motion, u z . rectangular components : vxav vyav vzav xx x yy y zz z && normal and tangential components: vu u au u u u uu = + & & & sv v dv ds v aa tt tn t n nn θ ρ 2 , 2 2 2 3 2 1 dx y d dx dy + = cylindrical components: ( ) ru u u u u = = + =− + + r rr v v r r r r r & & & & & θθ 2 2
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Mech 2 Dynamics Formula and Data Sheet Page 2 of 8 Rigid Body Kinematics Concept Formulae Rotation about a Fixed Axis: Same equations as rectilinear motion, substituting linear acceleration ( a ) with angular acceleration ( α ), linear speed, ( v ) with angular speed ( ω ), and distance, ( s ) with angle ( θ ). ω θ α αθ ωω == = d dt d dt dd for constant acceleration: () θα ωθ ωα ωω =+ + 1 2 2 2 00 0 2 0 2 0 c c c tt t Absolute General Plane Motion: Describe the position of the point in terms of absolute ( x, y ), ( r, θ ), or distance ( s or θ ) coordinates. Relate rectilinear and angular position via trigonometric equations, e.g. s=f ( ). Differentiate these equations to get ultimate relationships between v and ω , a and α . Do not make substitutions of numbers for variables until you have finished differentiating!
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This note was uploaded on 10/26/2010 for the course ENGINEERIN MECH221 taught by Professor Wetton during the Spring '10 term at The University of British Columbia.

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Electrical - MECH 2 Dynamics Formula and Data Sheet Some Standard Physical Constants Acceleration at Sea Level due to Gravity g = 9.81 m/s 2 Speed

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