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Unformatted text preview: Key to the success in this class Time : You need to spend enough hours on it. Learn smartly : Study groups, office hour, etc. Practice, practice, and practice: HMWK, Endof chapter problems Prelecture: Read the book before Postlecture: Read the book (slides) after Train yourself to think scientifically and independently Chapter 1: Vectors VS Scalars Concept of vector (VS scalar) Vector addition Unit vector notation Components of vectors Vector addition using components Vector decomposition * Products of vectors (covered in later chapters) Vectors: Magnitude and Direction Vectors show magnitude and displacement, drawn as a ray. A physics vector is quantity that has both magnitude (how long/how fast, etc) and direction Confused? You wont be the only One. Be patient and we will come back to this often If lost in a desert (forest) at P1, which quantity should you try to maximize (distance or displacement) Vector addition (consider your daily commuting route) Vectors may be added graphically, head to tail. Vector addition Example: A traveler hiked 1.00km north, then 2.00km to the west. What is the displacement (d) his ending position from the starting position? Vector addition Example: A traveler hiked 1.00km north, then 2.00km to the west. What is the displacement (d) his ending position from the starting position? d 2 = (1.00 km ) 2 + (2.00 km ) 2 d 2 = 5.00 km 2 d = 5.00 km tgf = 2.00 km 1.00 km = 2.00 f = tg 1 (2.00) = 63.4 o Components of vectors Manipulating vectors graphically is insightful but difficult when striving for numeric accuracy. Vector components provide a numeric method of representation. Any vector is built from an x component and a y component (and z). Any vector may be decomposed into its x component using V *cos and its y component using V *sin (where is the angle the vector V sweeps out from 0). Unit vectorsFigures Assume vectors of magnitude 1 with no units exist in each of the three standard dimensions. The x direction is termed i , the y direction is termed j , A vector is subsequently described by a scalar times each component. A = A x i + A y j = A cos i + A sin j Refer to Example 1.9. cos Vector addition Example II: A traveler hiked 5km at 37 degrees relative to the xaxis, then 10km at 53 degrees relative to the xaxis. What is the resultant Displacement? 37 o 53 o d 1 d 2 d = ? x y DECOMPOSE first! Vector addition Example II: d 1 = (5 km )cos 37 o x + (5 km )sin 37 o y = (4 km ) x + (3 km ) y r d 2 = (6 km ) x + (8 km ) y r d = r d 1 + r d 2 = (10 km ) x + (11 km ) y tgq = 11 km 10 km =1.1 q = tg 1 (1.1) = 47.7 o A traveler hiked 5km at 37 degrees relative to the xaxis, then 10km at 53 degrees relative to the xaxis. What is the resultant Displacement?...
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 Fall '09
 YIFU ZHU
 Physics

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