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eqnmidterm2 - Equations for Midterm 2 Physics 6A Winter...

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Equations for Midterm 2 Physics 6A, Winter 2008 Geometry Area of circle: A = πr 2 Circumfrence of circle: C = 2 πr Volume of sphere: V = 4 3 πr 3 Density: ρ = M V Vector Math For some vector vector r with components x and y : vector r = ( x, y ) Magnitude r = | vector r | = radicalbig x 2 + y 2 Angle θ = arctan ( y x ) x = r cos θ y = r sin θ vector r 1 + vector r 2 = ( x 1 + x 2 , y 1 + y 2 ) Velocity and Acceleration Average velocity: vector v = Δ vector x Δ t Displacement in case of constant velocity: x = x 0 + v x t Average acceleration: vector a = Δ vector v Δ t Velocity in case of constant acceleration: v x = v x 0 + a x t Displacement in case of constant acceleration: x = x 0 + v x 0 t + 1 2 a x t 2 Velocity, acceleration, and displacement: v 2 x = v 2 x 0 + 2 a x ( x - x 0 ) Relative velocity: Velocity of object B with respect to point/object A: v B | A Velocity of object C with respect to point/object B: v C | B Velocity of object C with respect to point/object A: v C | A = v C | B + v B | A Projectile motion: for initial velocity v 0 at some angle θ 0 : Horizontal range R = v 2 0 sin 2 θ 0 g Uniform Circular Motion: constant speed v c in a circle of radius
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