Abstract and Mathematical Techniques in General Physics I | PHYS 2010, Study notes of Physics

Download Abstract and Mathematical Techniques in General Physics I | PHYS 2010 and more Study notes Physics in PDF only on Docsity! PHYS-2010: General Physics I Course Lecture Notes Section II Dr. Donald G. Luttermoser East Tennessee State University Edition 2.4 Abstract These class notes are designed for use of the instructor and students of the course PHYS-2010: General Physics I taught by Dr. Donald Luttermoser at East Tennessee State University. These notes make reference to the College Physics, 8th Edition (2009) textbook by Serway and Vuille. Donald G. Luttermoser, ETSU II–3 d) Two common bases: i) Base 10 ⇒ common logarithms: log a = log10 ≡ log x = log y ⇐⇒ y = 10x . ii) Base e = 2.71828... ⇒ natural logarithms: log a = log e ≡ ln x = ln y ⇐⇒ y = ex . C. Basic Trigonometry. 1. Right-angle triangle relationships: a b c φ θ sin θ = a c , cos θ = b c , tan θ = a b = sin θ cos θ a2 + b2 = c2 or sin2 θ + cos2 θ = 1 θ + φ = 90◦ = π 2 radians. II–4 PHYS-2010: General Physics I 2. Generic triangle relationships: a b c A B C a) Law of sines: sin A a = sin B b = sin C c . b) Law of cosines: a2 = b2 + c2 − 2bc cos A , b2 = a2 + c2 − 2ac cos B , c2 = a2 + b2 − 2ab cos C . 3. Additional useful trigonometric identities. a) Angle-sum and angle-difference relations: sin(α + β) = sin α cos β + cos α sin β sin(α − β) = sin α cos β − cos α sin β cos(α + β) = cos α cos β − sin α sin β cos(α − β) = cos α cos β + sin α sin β tan(α + β) = tan α + tanβ 1 − tanα tanβ tan(α − β) = tan α − tanβ 1 + tanα tanβ Donald G. Luttermoser, ETSU II–5 b) Double-angle relations: sin 2α = 2 sin α cos α = 2 tan α 1 + tan2 α cos 2α = cos2 α − sin2 α = 2 cos2 α − 1 = 1 − 2 sin2 α = 1 − tan2 α 1 + tan2 α tan 2α = 2 tan α 1 − tan2 α D. Scalars and Vectors. 1. A scalar has magnitude but no directional information (e.g., c is a scalar). a) 4 kg and 600 K are scalars. b) 420 km/s is a scalar (i.e., speed). 2. A vector has both magnitude and directional information (e.g., ~c is a vector). a) 420 km/s to the NW is a vector (i.e., velocity). b) 420 km/s NW is not equal to 420 km/s SE! c) Note that in these course notes I will always represent a vector with an arrow over the variable letter (e.g., ~A), whereas your textbook indicates a vector with a boldface letter (e.g., A). d) Vector arthimetic will be described in §IV of the notes.