CH0102part2 - Key to the success in this class Time You...

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, End-of- chapter problems Pre-lecture: Read the book before Post-lecture: 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 won’t 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 θ and its y component using V *sin θ (where θ is the angle the vector V sweeps out from 0°). Unit vectors—Figures • 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 θ i + A sin θ j • Refer to Example 1.9. cos θ Vector addition Example II: A traveler hiked 5km at 37 degrees relative to the x-axis, then 10km at 53 degrees relative to the x-axis. What is the resultant Displacement? 37 o 53 o ρ d 1 ρ d 2 ρ d = ? θ x y DECOMPOSE first! Vector addition Example II: ρ d 1 = (5 km )cos 37 o ö x + (5 km )sin 37 o ö y = (4 km ) ö x + (3 km ) ö y r d 2 = (6 km ) ö x + (8 km ) ö y r d = r d 1 + r d 2 = (10 km ) ö x + (11 km ) ö 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 x-axis, then 10km at 53 degrees relative to the x-axis. What is the resultant Displacement?...
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