1. Chapter 1: Measurement and vectors
Phys 201, Spring 2011 Chapt. 1, Lect. 2
Chapter 1: Measurement and vectors
Reminders:
The grace period of WebAssign access is two weeks.
2. The lab manual can be viewed online, but you are
recommended to buy a hard copy from the bookstore.
For honors credit, attend Friday’s 207 lecture,
TOMORROW 12:05pm, (or write an essay later).
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Phys 201, Spring 2011

2. Review from last time:  Units: Stick with SI, do proper conversion.
(in each equation, all terms must match!)
Dimensionality: any quantity in terms of
L, T, M (the dimension for basic units).
Significant figures (digits) and errors
Estimate (rounding off to integer)
and order of magnitude (to 10’s power)
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Phys 201, Spring 2011

3. The density of seawater was measured to be 1. 07 g/cm3
The density of seawater was measured to be 1.07 g/cm3. This density in SI units is
1.07 kg/m3
(1/1.07) x 103 kg/m3
1.07 x 103 kg
1.07 x 10–3 kg
1.07 x 103 kg/m3
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Phys 201, Spring 2011

4. The density of seawater was measured to be 1. 07 g/cm3
The density of seawater was measured to be 1.07 g/cm3. This density in SI units is
1.07 kg/m3
(1/1.07) x 103 kg/m3
1.07 x 103 kg
1.07 x 10–3 kg
1.07 x 103 kg/m3
An order of magnitude estimate: 1 tonne /m3
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Phys 201, Spring 2011

5. If K has dimensions ML2/T2, then k in the equation K = kmv2 must
have the dimensions ML/T2.
have the dimension M.
have the dimensions L/T2.
have the dimensions L2/T2.
be dimensionless.
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Phys 201, Spring 2011

6. If K has dimensions ML2/T2, then k in the equation K = kmv2 must
have the dimensions ML/T2.
have the dimension M.
have the dimensions L/T2.
have the dimensions L2/T2.
be dimensionless.
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Phys 201, Spring 2011

7. Today: Vectors
In one dimension, we can specify distance with a real number, including + or – sign (or forward-backward).
In two or three dimensions, we need more than one number to specify how points in space are separated – need magnitude and direction.
Madison, WI and Kalamazoo, MI are each about 150 miles from Chicago.
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Phys 201, Spring 2011

8. Scalars, vectors: Denoting vectors Two of the ways to denote vectors:
Scalars are those quantities with magnitude, but no direction:
Mass, volume, time, temperature (could have +- sign) …
Vectors are those with both magnitude AND direction:
Displacement, velocity, forces …
Denoting vectors
Two of the ways to denote vectors:
Boldface notation: A
“Arrow” notation:
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Phys 201, Spring 2011

9. Example: Displacement (position change)
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10. Adding displacement vectors
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11. “Head-to-tail” method for adding vectors
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12. Vector addition is commutative
Vectors “movable”: the absolute position is less a concern.
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13. Adding three vectors: vector addition is associative.
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14. A vector’s inverse has the same magnitude and opposite direction.
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15. Subtracting vectors
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16. Example 1-8. What is your displacement if you walk 3
Example What is your displacement if you walk 3.00 km due east and 4.00 km due north?
Pythagorean theorem
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17. Components of a vector along x and y
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18. Components of a vector: along an arbitrary direction
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19. Magnitude and direction of a vector
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20. Adding vectors using components
Cx = Ax + Bx
Cy = Ay + By
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21. Unit vectors The unit vector along x is denoted
The unit vector along y is denoted
The unit vector along z is denoted
A unit vector is a dimensionless vector with magnitude exactly equal to one.
aaa
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22. Which of the following vector equations correctly describes the relationship among the vectors shown in the figure?
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23. Which of the following vector equations correctly describes the relationship among the vectors shown in the figure?
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24. Can a vector have a component bigger than its magnitude?
Yes No
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25. Can a vector have a component bigger than its magnitude?
Yes No
The square of a magnitude of a vector R is given in terms of its components by
R2 = Rx2 + Ry2 .
Since the square is always positive, no component can be larger than the magnitude of the vector.
Thus, a triangle relation:
| A | + | B | > | A+B |
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26. Properties of vectors: summary
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