Equations x f xi 12 v xi v xf t f ti y f yi 12 v yi v yf t f ti x f xi v xi t f ti 12 ax t f ti 2 y f yi v yi t f ti 12 ay t f ti v xf v xi ax t f ti v yf v yi ay t f ti v 2xf v 2xi 2ax x f xi cos x v 2yf v 2yi 2ay y f yi g 9 80 m a y g y s2 sin y h x x f xi x t 0 t v x lim h x xi v x avg f t f ti 32 2 ft s2 tan y a avg f Smax S N 1 2 mv 2 v f vi t f ti v x t 0 t z b b 2 4ac 2a F ma K h x 2 y2 x ax lim az 2 bz c 0 ar v 2 r 2 FG f k k N v v v o Gm1m 2 mg 2 r Fx kx r r vot W F cos d K f K i Density Mass volume M V G 6 67x10 11 Nm2 kg 2 Rearth 6 37 10 3 km M earth 5 97 10 24 kg U g mgy E K U U s 12 kx 2 W c U Pavg W t Pavg Fv W NC E f E i p mv I Favg t I p f pi m1 m2 2m1 v1 f v2 f v1i v1i m1 m2 m1 m2 mi x i m v p i i x cm v cm Fext t mi mi f i i lim avg f t 0 t t f ti t f ti 2 lim T v t r at r t 0 t f i 12 i f t f t i s r avg f i i t f t i 12 t f t i 2 f i t f ti 2f i2 2 f i rF sin I I mi ri2 K R 12 I 2 i P 2 r 3 2 T GM L t v GM r I ICM MD2 L I W R Moments of inertia about axes through the center of mass I hoop MR 2 I disk 12 MR 2 I hollow sphere 23 MR 2 x A cos t I solid sphere 25 MR 2 T m f 1 2 f T 2 v A sin t k I rod 121 ML2 a A cos t g L 2 2 I MgL Sphere surface area 4 r 2 volume 43 r 3 Circle area r 2 circumference 2 r
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