equations_2_f4

equations_2_f4 - Angular Velocity: t + = Angle, as function...

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Some Mathematics Quadratic formula: The general solution of an equation 0 2 = + + c bx ax is given by the quadratic formula: . 2 4 2 a ac b b x - ± - = Useful formula: ) )( ( ) ( 2 2 b a b a b a + - = - Trigonometry: . cos sin tan ; cos ; sin α = = = = a o h a h o Radians and degrees: 0 360 2 = π First Newton’s Law: . ; 0 const v F = = Second Newton’s Law: = = a m F F net Third Newton’s Law 21 12 F F - = Forces : gravity = mg; F N normal force (always perpendicular to the support or contact); tension force; friction force: . ; N K N S F kinetic F static μ = = Circular Motion : r r v l centripeta a 2 2 ) ( ϖ = = h a o α
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Newton’s Law of Universal Gravitation : 2 2 11 2 2 1 / 10 67 . 6 ; kg m N G r m m G F × = = - Work and Energy: θ cos Fd W = ; Kinetic energy : . 2 2 mv KE = The Work-Energy Principle : KE W net = . Gravitational Potential Energy : mgh PE grav = ; h – vertical height above some reference level. Elastic Potential Energy : 2 2 kx PE elastic = ; k – elastic constant (spring constant). Momentum : . v m p = Impulse: . ) ( ) ( ) ( initial final v m v m v m t F - = = Coordinates of Center of Mass : . ... .... 2 1 2 2 1 1 n n n CM m m m m x m x m x x + + + + + + = Same for y and z-coordinates. Rotational Motion, Angular Quantities(uniformly accelerated rotational motion):
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Unformatted text preview: Angular Velocity: t + = Angle, as function of time: . 2 1 2 t t + = 2 2 2 2 + = + = Linear velocity through angular one : r v = Tangential acceleration through angular one: r a gent = tan Period of Rotation: f T 1 2 = = Torque: ; sin rF = . Newtons Second Law for Rotation : I = . Elastic Collision: V 1(initial) - V 2(initial) =V 2(final) -V 1(final) Rotational Kinetic Energy : . 2 1 2 I KE rotational = Angular Momentum: . I L = Newtons Second Law in Terms of Angular Momentum : t L = Moments of Inertia: Solid cylinder or disk: MR 2 /2 Thin rod (of length L) with rotation axis through center: ML 2 /12....
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equations_2_f4 - Angular Velocity: t + = Angle, as function...

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