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Frames of ReferenceFrames of Reference
 Object or point from which motion isObject or point from which motion is
determineddetermined
 Most common is theMost common is the
EarthEarth
 Motion is a changeMotion is a change
inin positionposition relativerelative toto
a frame of referencea frame of reference
What is motion?What is motion?
 If you are standing in one place, and your friendIf you are standing in one place, and your friend
walks by you.walks by you.
 Are you moving relative to your friend?Are you moving relative to your friend?
 Is your friend moving relative to you?Is your friend moving relative to you?
 Are either of you moving relative to the earth?Are either of you moving relative to the earth?
Answer:Answer:
 You are moving relative to your friend, andYou are moving relative to your friend, and
your friend is moving relative to you!your friend is moving relative to you!
 You are not moving relative to the earth,You are not moving relative to the earth,
but your friend is. You are both movingbut your friend is. You are both moving
relative to the sun!relative to the sun!
What is motion?What is motion?
 If you and your friend are walking down the hallIf you and your friend are walking down the hall
together at the same speed, in the same directiontogether at the same speed, in the same direction
 Are you moving relative to your friend?Are you moving relative to your friend?
 Is your friend moving relative to you?Is your friend moving relative to you?
 Are either of you moving relative to the Earth?Are either of you moving relative to the Earth?
Answer:Answer:
 You are NOT moving relative to yourYou are NOT moving relative to your
friend, and your friend is NOT movingfriend, and your friend is NOT moving
relative to you. You both are movingrelative to you. You both are moving
relative to the earth.relative to the earth.
Explanation
 Distance is the actual length measured
of a particular path taken.
 Displacement is the length and
direction of a straight line drawn from
the start to finish.
Evaluation
Distance vs. Displacement HO 1.5
Explanation
What’s your Vector?
 The most important distinction between
“distance” and “displacement” is that distance is
a scalar and displacement is a vector.
 Scalars are simple magnitudes.
 15 apples
 135 miles
 Vectors contain information about the magnitude
(size) and direction of a physical observable.
 64 miles Southwest
 Vectors are typically depicted as arrows drawn
with a specific length and pointing in a specific
direction.
your
home
your
school
A displacement has
Size = length
of this arrow
displacement from
home to school
displacement from
home to school
2 Displacement and
distance
To go to school from home...
size & direction.
Distance = length of path
you travelled
(≠ size of displacement)
l1l2
l3
2 Displacement and
distance
To go to school from home...
your
home
your
school
= l1 + l2 + l3
Elaboration
What’s your Vector?
 A car travels 6 miles East and then 8 miles North.
 Determine the distance traveled by the car.
 Draw and describe the displacement vector of the car.
6 mi E
8 mi N
10mi
53o
N of E
So the car’s
displacement is 10
miles NE
Conclusion
Summary of Concepts
 Distance is the length of the path traveled.
 Displacement (from “dis”-place to “dat”-place)
is the length and direction of a line from start
to finish.
 Motion is a change in position relative to a
point of reference.
 Distance is a scalar quantity that contains only
magnitude
 Displacement is a vector quantity that
contains both magnitude and direction.
total distance = ?
total displacement = ?
3km + 4km = 7 km
total distance
total displacement
3km north + 4km north
= 7 km north
N
4 km
7 km
north
3 km
Adding displacements
A car travels 4 km northA car travels 4 km north then 3 km north.
4 Adding displacements
A car travels 4 km northA car travels 4 km north then 3 km south.
4 km
1 km
north
3 km
total distance = ?
total displacement = ?
= 3km + 4km = 7 km
total distance
total displacement
= −3km south + 4km north
= 1 km north
N
a Graphical method
4 Adding displacements
A car travels 4 km northA car travels 4 km north then 3 km east.
4 km
3 km
φ 5 km
total distance = ?
total displacement = ?
= 3km + 4km = 7 km
total distance
total displacement
N
a Graphical method
d2
= 32
+ 42
d =5 km NE
‘tip’ of p joined to ‘tail’ of q
p
q
p + q
Tip-to-tail method:
Graphing

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Motion

  • 1.
  • 2. Frames of ReferenceFrames of Reference  Object or point from which motion isObject or point from which motion is determineddetermined  Most common is theMost common is the EarthEarth  Motion is a changeMotion is a change inin positionposition relativerelative toto a frame of referencea frame of reference
  • 3. What is motion?What is motion?  If you are standing in one place, and your friendIf you are standing in one place, and your friend walks by you.walks by you.  Are you moving relative to your friend?Are you moving relative to your friend?  Is your friend moving relative to you?Is your friend moving relative to you?  Are either of you moving relative to the earth?Are either of you moving relative to the earth?
  • 4. Answer:Answer:  You are moving relative to your friend, andYou are moving relative to your friend, and your friend is moving relative to you!your friend is moving relative to you!  You are not moving relative to the earth,You are not moving relative to the earth, but your friend is. You are both movingbut your friend is. You are both moving relative to the sun!relative to the sun!
  • 5. What is motion?What is motion?  If you and your friend are walking down the hallIf you and your friend are walking down the hall together at the same speed, in the same directiontogether at the same speed, in the same direction  Are you moving relative to your friend?Are you moving relative to your friend?  Is your friend moving relative to you?Is your friend moving relative to you?  Are either of you moving relative to the Earth?Are either of you moving relative to the Earth?
  • 6. Answer:Answer:  You are NOT moving relative to yourYou are NOT moving relative to your friend, and your friend is NOT movingfriend, and your friend is NOT moving relative to you. You both are movingrelative to you. You both are moving relative to the earth.relative to the earth.
  • 7. Explanation  Distance is the actual length measured of a particular path taken.  Displacement is the length and direction of a straight line drawn from the start to finish.
  • 9. Explanation What’s your Vector?  The most important distinction between “distance” and “displacement” is that distance is a scalar and displacement is a vector.  Scalars are simple magnitudes.  15 apples  135 miles  Vectors contain information about the magnitude (size) and direction of a physical observable.  64 miles Southwest  Vectors are typically depicted as arrows drawn with a specific length and pointing in a specific direction.
  • 10. your home your school A displacement has Size = length of this arrow displacement from home to school displacement from home to school 2 Displacement and distance To go to school from home... size & direction.
  • 11. Distance = length of path you travelled (≠ size of displacement) l1l2 l3 2 Displacement and distance To go to school from home... your home your school = l1 + l2 + l3
  • 12. Elaboration What’s your Vector?  A car travels 6 miles East and then 8 miles North.  Determine the distance traveled by the car.  Draw and describe the displacement vector of the car. 6 mi E 8 mi N 10mi 53o N of E So the car’s displacement is 10 miles NE
  • 13. Conclusion Summary of Concepts  Distance is the length of the path traveled.  Displacement (from “dis”-place to “dat”-place) is the length and direction of a line from start to finish.  Motion is a change in position relative to a point of reference.  Distance is a scalar quantity that contains only magnitude  Displacement is a vector quantity that contains both magnitude and direction.
  • 14. total distance = ? total displacement = ? 3km + 4km = 7 km total distance total displacement 3km north + 4km north = 7 km north N 4 km 7 km north 3 km Adding displacements A car travels 4 km northA car travels 4 km north then 3 km north.
  • 15. 4 Adding displacements A car travels 4 km northA car travels 4 km north then 3 km south. 4 km 1 km north 3 km total distance = ? total displacement = ? = 3km + 4km = 7 km total distance total displacement = −3km south + 4km north = 1 km north N a Graphical method
  • 16. 4 Adding displacements A car travels 4 km northA car travels 4 km north then 3 km east. 4 km 3 km φ 5 km total distance = ? total displacement = ? = 3km + 4km = 7 km total distance total displacement N a Graphical method d2 = 32 + 42 d =5 km NE
  • 17. ‘tip’ of p joined to ‘tail’ of q p q p + q Tip-to-tail method: Graphing

Editor's Notes

  1. Take a moment to distinguish the difference between the two terms Take three paces to the right and ask the students to estimate both distance and displacement Displacement should include direction from “dis”-place to “dat”-place Now go back to the starting point and take three paces to the left What changed? The distance is the same but the displacement is in another direction
  2. Have students measure both distance and displacement on the treasure map (They will have to create a legend)
  3. Have students list scalar quantities Money, Time, Energy, Objects, etc… From Geometry, what would we call a line that starts at a point, has a certain length, and points in one direction: ray
  4. Have students follow along on vector guide Remind them of Pythagorean Theorem If desired, model the use of trigonometry and a calculator to determine the angle
  5. Slowly reiterate the important points and ask for questions. Remember to wait at least 3 seconds before moving on. Ask if there are any new vocabulary words that need to be redefined or written on the board (we all have to speak the same language)