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PHY121_Formulae_M2

# PHY121_Formulae_M2 - Formulae Vectors A = Axi Ayj with i(j...

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Formulae: Vectors: A = A x i + A y j with: i ( j ) the unit vector along the x ( y ) axis Trigonometry: sin θ b/c ; cos θ a/c ; tan θ b/a = “slope” of c thus: b=c sin θ , a=c cos θ , b=a tan θ , a 2 + b 2 = c 2 , hence: sin 2 θ + sin 2 θ = 1 sin θ = cos(90° θ ), sin θ = sin( θ ), cos θ = cos( θ ) sin30° = cos60° = ½ sin60° = cos30° = ½ 3 sin45° = cos45° = ½ 2, tan45° = 1 Components: (if θ angle with the + x -axis!) A x =A cos θ ; A y =A sin θ ; A = ( A x , A y ) Scalar Product (“Dot” Product): ( θ A , B angle between the vectors A and B ) A · B A x B x + A y B y = AB cos θ A , B = AB // = A // B Uncertainty:  22 ;; S A BS A B S c AS c A S A S A A B B         Kinematics: the “motion”: position s as function of time t s = s ( t ) = ( x , y ) (position) velocity v ; acceleration a : v d s / dt = ( v x , v y ); speed v | v | ; a d v / dt= ( a x , a y ) Linear motion with constant a : v = v 0 + a t, s = s 0 + v 0 t + ½ a t 2 ; eliminating t : v 2 = v 0 2 + 2 a ·( s s 0 ) rotation angle (radians; rotation radius R ): s (=arc length) /R = ( t ) (angular position) angular velocity :

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PHY121_Formulae_M2 - Formulae Vectors A = Axi Ayj with i(j...

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