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Formula Sheet Cascarano Scalar Product Math Stuff ββ = |π΄β||π΅ ββ| cos π π΄β β π΅ Vector Product ββ = |π΄β||π΅ ββ| sin π π΄β × π΅ Quadratic formula (ax2+bx+c=0) π₯= Kinematics π£π₯ = π£ππ₯ + ππ₯ π‘ 1 π₯ = π₯π + π£ππ₯ π‘ + 2ππ₯ π‘ 2 2 π£π₯2 = π£ππ₯ + 2ππ₯ (π₯ β π₯π ) π£ππ₯ + π£π₯ π₯ β π₯π = ( )π‘ 2 Velocity Addition π£βπ΄π΅ = π£βπ΄πΆ + π£βπΆπ΅ βπ ± βπ 2 β 4ππ 2π Acceleration of gravity Constants g = 9.80 m/s2 G = 6.67x10-11 Nm2/kg2 Universal gravitation ππΈ = 5.97π₯1024 ππ π πΈ = 6.38π₯106 π Mass of Earth Radius of Earth Trig Identities Law of cosines: Newtonβs Laws / Friction / Circular motion βπβ 2 Law β πΉβ = ππβ = π2 = π 2 + π 2 β 2ππ cos πΌ Gravitation Law of sines: Static friction Kinetic friction nd βπ‘ π π π = = sin πΌ sin π½ sin πΎ ο§ a ο’ b ο‘ πΊπ1 π2 πΉ= π2 ππ β€ ππ π ππ = ππ π Centripetal acceleration πππ = 1 Work done by a spring ππ π = 2ππ₯ 2 Conservative forces ππ = ββπ Non-conservative forces Power πππ = βπΈ ππππ π= π‘πππ Impulse and Momentum πβ = ππ£β Energy 1 πΎ = 2ππ£ 2 Kinetic energy Gravitational potential energy Spring potential energy Impulse momentum ππ = πππ¦ = β πΊπππΈ π 1 ππ π = 2ππ₯ 2 πΉ = ππ₯ ππ‘ππ‘ππ = βπΎ Hookeβs Law (spring force) Work-Energy Theorem Center of Mass Center of mass (point objects) π₯πΆπ = πΌβ = πΉβππ£π βπ‘ πΌβ = βπβ Impulse π£2 π c Work & Power π = πΉππππ π Work by constant force Linear momentum Physics 2A βπ ππ π₯π βπ π π πβπ‘ππ‘ππ = ππ‘ππ‘ππ π£βπΆπ Total momentum β πΉβππ₯π‘ = ππ‘ππ‘ππ πβπΆπ Rotational Kinematics π = ππ + πΌπ‘ 1 Linear / Angular π = ππ (π ππ πππππππ ) π = ππ + ππ π‘ + 2πΌπ‘ 2 π£π‘ = ππ π2 = ππ2 + 2πΌ(π β ππ ) ππ + π π β ππ = ( )π‘ 2 ππ‘ = ππΌ Torque πππ = π£2 = ππ2 π Torque and Angular Momentum πβ = πβ × πΉβ = ππΉπ ππβ = πβ₯ πΉ Angular momentum πΏββ = πβ × πβ = ππ£πβ₯ = πΌπ ββ Rotational Inertia and Energy πΌ = βπ ππ ππ 2 Rotational inertia (point objects) Parallel axis theorem πΌπ = πΌπΆπ + ππ 2 1 πΎ = 2πΌπ2 Rotational kinetic energy Rotational Motion Newtonβs 2nd law β πβ = πΌπΌβ = ββ ππΏ ππ‘ Work π = πβπ = βπΎπππ‘ Power π = ππ Cascarano Displacement Formula Sheet Simple Harmonic Motion π₯(π‘) = π΄πππ (ππ‘ + β ) Velocity Period Angular Frequency Mass on a spring Simple pendulum π£(π‘) = βππ΄π ππ(ππ‘ + β ) 2π π= π Frequency (j) Thin hoop rotating on axis through any diameter of the hoop: 1 πΌ = ππ 2 2 Physics 2A π π=β π π π=β π 1 π π= = π 2π