University Physics with Modern Physics with Mastering Physics (11th Edition)

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Formulae: Vectors: A = A x i + A y j + A z k Scalar Product (“Dot” Product) A · B = A x B x + A y B y + A z B z = AB cos θ A , B Kinematics: the “motion” r = r ( t ) (position) velocity v d r / dt (speed | v | ) acceleration a d v / dt Linear Kinematics for CONSTANT a v = v 0 + a t, r = r 0 + v 0 t + ½ a t 2 ; eliminating t : v 2 = v 0 2 + 2 a ·( r r 0 ) Angle θ (in radians): θ s (=arc length) /R Angular velocity ω ; angular acceleration α : ω v T /R ; α a T /R ( T = Tangential) Circular motion with CONSTANT α , radius R : ω = ω 0 + α t; θ = θ 0 + ω 0 t + ½ α t 2 ; eliminating t : ω 2 = ω 0 2 + 2 α ( θ θ 0 ) Uniform circular motion - acceleration: a = a c = a rad = v T 2 / R (inwards) Force and its consequences: Σ F i = m a and F A on B = –F B on A Examples of forces: Force of Gravity (on mass
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Unformatted text preview: j ) (downwards) ( g = 9.80 m/s 2 ) Force of a spring (spring constant k ): F S = – k x (opposes displacement x ) Friction: Static Friction: F f ≤ µ s N Kinetic friction: F f = k N =coef. of friction; N =normal force Friction opposes the motion Equilibrium: Σ F i = 0 Work done by a force F over a trajectory: W F ≡ ∫ F ⋅ d x Kinetic Energy K : K ≡ ½ mv 2 Work-Kinetic Energy relationship (using Σ F i = m a ) W tot = Σ W i = ∆ K ≡ K f – K i Power P (of force F ): P F ≡ dW F /dt = F·v...
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