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Unformatted text preview: Carnegie Mellon University Physics Department 33106 Fall08 Roy A. Briere Exam I Review Items Chapter 1: Units, Scalars, Vectors, ... Physical quantities have a “type”: scalar and vector are enough for us. If asked for a vector (velocity, momentum, ...): • Give components, or magnitude plus direction, not just magnitude ! They also have a dimension, such as length, or length per time squared. Understand issues with and the difference between units and dimensions: • Even if we know dimension, we still have to consider units: a length may be measured in meters, feet, furlongs, cm, ... It is safest to convert to standard SI (“mks”) units: m, kg, s. (cm, km, and are all common, but nonstandard) For us, most new SI units will be combinations of these • Be careful to distinguish between scalars and vectors • Review the textbook’s discussion on significant figures As new quantities are introduced in the rest of the course: • Know which quantities are vectors, and which are scalars • For example (later on): Is energy a scalar or vector? What about momentum? • Always think about what signs mean ( < 0 vs. > 0), and also zero Certain manipulations are common enough to list as general mathematical “tools” that should eventually become as routine as basic algebra: 1) Practice manipulating dimensions: • Q: What is a velocity squared divided by a distance? A: an acceleration 2) Know how to use dot (scalar) products to calculate angles • cos θ = A · B/  A   B  ) • Evaluate with components to find cos θ 3) Make a unit vector from any vector A • Do scalar multiplication by A by 1 /  A  • In other words, ˆ A = A/  A  4) For a two dimensional vector A = A x ˆ i + A y ˆ j , notice the useful fact that • B = A y ˆ i + A x ˆ j is perpendicular to A (“swap components and negate one) • True, since A · B = 0 (thus B = + A y ˆ i A x ˆ j is also perpendicular) 5) Scaling to any length (including unit length, but more general now) • Imagine we wish that A was stretched or shrunken so that it had magnitude m , instead of it’s current value  A  • You should be able to see that the new vector B = ( m/  A  ) A has magnitude  A  = m and is parallel to B . Chapter 2: OneDimensional Kinematics Try to use specific variables: •...
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 Spring '10
 MAJESTIC
 Physics, Vector Space, Dot Product, Acceleration, Momentum

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