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PH 201

PH 201. Dr. Cecilia Vogel Lecture 4. REVIEW. Acceleration and graphs derivatives Constant acceleration x vs t, v vs t, v vs x. OUTLINE. Vectors notation magnitude and direction components vector equations. Vectors.

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PH 201

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  1. PH 201 Dr. Cecilia Vogel Lecture 4

  2. REVIEW • Acceleration and graphs • derivatives • Constant acceleration • x vs t, v vs t, v vs x OUTLINE • Vectors • notation • magnitude and direction • components • vector equations

  3. Vectors • In one dimension, you can describe a vector by a number & a sign. In 2-D or 3-D that’s not enough. • In 2-D, you need to give _____2____ numbers with signs, in 3-D, need ___3_____ • For example, surface of Earth is 2-D, need to give latitude and longitude

  4. (4,5) (0,0) Vectors in 2-D (6,11) (2,6) • Both these vectors are described by y-component x-component

  5. (4,5) (0,0) Length of Vector

  6. Components of Vector If the vector has length A and direction angle q measured counterclockwise from the +x-axis, then Ax=Acos(q) = x-component of vector A Ay=Asin(q) = y-component of vector A

  7. Size and direction of Vector If the vector has x-component Ax and y-component Ay, then the magnitude of the vector is A=sqrt(Ax2+Ay2) the direction angle is q=tan-1(Ay/Ax) IF the angle is in the first quadrant. If not, you may have to adjust to the correct quadrant (because your calculator can’t tell the diff between -4/3 and 4/-3, for example).

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