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Welcome back to Physics 211

Welcome back to Physics 211. Today’s agenda: Review Vectors Vector components. ConcepTest 8. You are throwing a ball…. Acceleration of ball rolling on incline. Acceleration is not zero at top. velocity. time. Vectors. are used to denote quantities that have magnitude and direction

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Welcome back to Physics 211

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  1. Welcome back to Physics 211 Today’s agenda: Review Vectors Vector components

  2. ConcepTest 8 You are throwing a ball…

  3. Acceleration of ball rolling on incline

  4. Acceleration is not zero at top velocity time

  5. Vectors • are used to denote quantities that have magnitude and direction • can be added and subtracted • can be multiplied or divided by a number • can be manipulated graphically (i.e., by drawing them) or algebraically (usually by considering components)

  6. Examples • Numbers: temperature, pressure, volume …. • Vectors: position, velocity, force

  7. Adding vectors To add vector B to vector A: Draw vector A. Draw vector B with its tail starting from the tip of A. The sum vector A+B is the vector drawn from the tail of vector A to the tip of vector B.

  8. Multiplying vector by number x 2.0 = x –1 =

  9. Find the vector “B – A” 1. 2. 3. 4.

  10. Two unknown vectors A and B are added. The magnitude of the sum vector “A + B” (i.e., the quantity |A + B|) 1. is at least as great as |A| (i.e., the magnitude of A). 2. is at most as great as |A| + |B| (i.e., the magnitudes of A and B added). 3. must be equal to |A| + |B|. 4. can be greater than |A| + |B|.

  11. Projection of a vector Component of a vector “How much a vector acts along some arbitrary direction” Projection onto one of the coordinate axes (x, y, z)

  12. Components y A=Ax+Ay A A=axi+ayj Ay q i unit vector in x direction x Ax j unit vector in y direction ax,ay components of vector A Projection of A along coordinate axes

  13. More components • Note: ax=|A|cosq, ay=|A|sinq • |A|2=ax2+ay2

  14. Why components useful ? • Addition: just add components if C=A+B cx=ax+bx; cy=ay+by • Magnitude |A|2=ax2+ay2 • Direction tanq=ay/ax

  15. Use projector and meterstick

  16. A bird is flying along a straight line in a direction somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started. How far to the East is it from its starting point? 1. 0 miles 2. 0.5 miles 3. 1.0 mile 4. 1.5 miles

  17. 2D Motion Note: component of position vector along x direction is the x coordinate! s – vector position s=xi+yj

  18. Describing motion with vectors • Positions and displacements s,Ds = sfinal - sinitial • Velocities and changes in velocity: vave= ––––,vinst= lim ––––, Dv = vfinal - vinitial • Acceleration: aave= ––––,ainst= lim ––––, Dt0 Dt0

  19. Quick Quiz 3.3(from: Serway/Beichner, Physics) Can any component of a vector ever be greater than the magnitude of the vector? 1. Yes 2. No 3. Not sure

  20. Quick Quiz 3.4(from: Serway/Beichner, Physics) If one component of a vector is not zero, can the magnitude of the vector be zero? 1. Yes 2. No 3. Not sure

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