physics lesson 5 two dimensional motion and vectors eleanor roosevelt high school mr. chin-sung lin
TRANSCRIPT
![Page 1: Physics Lesson 5 Two Dimensional Motion and Vectors Eleanor Roosevelt High School Mr. Chin-Sung Lin](https://reader036.vdocuments.us/reader036/viewer/2022070410/56649ea95503460f94bae203/html5/thumbnails/1.jpg)
Physics Lesson 5
Two Dimensional Motion and Vectors
Eleanor Roosevelt High School
Mr. Chin-Sung Lin
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Two Dimensional Motion and Vectors
Scalars & Vectors
Vector Representation
One-Dimensional Vector Addition
Two-Dimensional Vector Addition
Vector Resolution
Vector Addition Through Resolution
Vector Application: Relative Velocity
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Scalars & Vectors
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Scalars & Vectors
Comparison of Scalars & Vectors
Scalars Vectors
Magnitude Magnitude
Direction
Physical Quantities
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Comparison of Scalars & Vectors
Scalars Vectors
Magnitude Magnitude
Direction
Physical Quantities
3 m/s
60o
Scalars & Vectors
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Examples of Scalars & Vectors
Scalars Vectors
Physical Quantities
Scalars & Vectors
displacement
velocity
acceleration
force
distance
speed
acceleration
mass
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Vector Representation
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Arrows
An arrow is used to represent the magnitude and direction of a vector quantity
Magnitude: the length of the arrow
Direction: the direction of the arrow
Head
Tail
Magnitude
Direction
Vector Representation
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Equality of Vectors
Vectors are equal when they have the same magnitude and direction, irrespective of their point of origin
Magnitude
Direction
Vector Representation
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Negative Vectors
A vector having the same magnitude but opposite direction to a vector
A
Vector Representation
- A
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One-Dimensional Vector Addition
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Vector Addition (Same Direction)
The result of adding two vectors (resultant) with the same direction is the sum of the two magnitudes and the same direction
One-Dimensional Vector Addition
10 m
5 m 5 m
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Vector Addition (Opposite Directions)
The result of adding two vectors (resultant) with opposite directions is the difference of the two magnitudes and the direction of the longer one
One-Dimensional Vector Addition
10 m
-5 m
5 m
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Two-Dimensional Vector Addition
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Vector Addition (Parallelogram Method)
The resultant is the diagonal of the parallelogram described by the two vectors
Two-Dimensional Vector Addition
ResultantB
A
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Vector Addition (Head-Tail Method)
Many vectors can be added together by drawing the successive vectors in a head-to-tail fashion. The resultant is from the tail of the first vector to the head of the last vector
Two-Dimensional Vector Addition
ResultantB
A
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Vector Subtraction
One vector subtracts another vector is the same as one vector adds another negative vector
Two-Dimensional Vector Addition
A
A – B = A + (-B)
B
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Vector Subtraction
One vector subtracts another vector is the same as one vector adds another negative vector
Two-Dimensional Vector Addition
Resultant- B
A
A – B = A + (-B)
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Vector Resolution
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Component Vectors
Any vector can be resolved into two component vectors (vertical and horizontal components) at right angle to each other
Vector Resolution
Horizontal component
Vector Vertical component
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Component Vectors
The process of determining the components of a vector is called vector resolution
Vector Resolution
Horizontal component
Vector Vertical component
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Calculate Component Vectors
The magnitude of the horizontal component vx = v cos θ
The magnitude of the vertical component vy = v sin θ
Vector Resolution
Vx = V cos θ
VVy = V sin θ
θ
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Two-dimensional vector addition
through vector resolution
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Two-Dimensional Vectors Addition
Resolve vectors into horizontal and vertical components
Add all the horizontal components of the vectors
Add all the vertical components of the vectors.
Find the final resultant by adding the horizontal and vertical components of the final resultant
Vector Addition through Resolution
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Two-Dimensional Vectors Addition
Vector Addition through Resolution
Ax
AAy
By
R
Bx
B
Rx
Ry
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Two-Dimensional Vectors Addition
Vector Addition through Resolution
34.6 m/s
40.0 m/s20.0 m/s
-26.0 m/s
-15.0 m/s
30.0
m/s
19.6 m/s
-6.0 m/s
30o
60o
20.5 m/s
-16.9o
34.6 m/s – 15.0 m/s = 19.6 m/s
20.0 m/s – 26.0 m/s = -6.0 m/s
tan-1 (-6.0 m/s /19.6 m/s) = -16.9o
sqrt (19.62 + 6.02) m/s = 20.5 m/s-30.0 m/s sin (60o) = -26.0 m/s
-30.0 m/s cos (60o) = -15.0 m/s
40.0 m/s sin (30o) = 20.0 m/s
40.0 m/s cos (30o) = 34.6 m/s
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Vector Application:Relative Motion
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Relative Velocity
Relative velocity is the vector difference between the velocities of two objects in the same coordinate system
Vector Application
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Relative Velocity
For example, if the velocities of particles A and B are vA and vB respectively in the same coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B) is vA – vB
VA VA – VB
VB
Vector Application
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Relative Velocity
The relative velocity vector calculation for both one- and two-dimensional motion are similar
The velocity vector subtraction (vA – vB ) can be viewed as vector addition (vA + (–vB))
Vector Application
VA VA +(–VB)
-VB
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Relative Velocity
Conversely the velocity of B relative to A is vB – vA
Vector Application
VA VB – VA
VB
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Q & A
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The End