3 vectors in physics 3-1 scalars versus vectors scalar: a number with unit volume, time,...
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3 Vectors in Physics3-1 Scalars versus Vectors
Scalar: a number with unit
volume, time, temperature, distance …
Vector: a mathematical quantity with both direction and magnitude
velocity, acceleration, displacement …
(1) Vector: draw diagram or sketch
Magnitude: length of line
Direction: arrow
(2) Vector: write
Boldface, r
Draw arrow over the vector’s symbol
Magnitude: r=|r|=| |
θ
x
y
r
r
r
3-2 The component of vector
Resolve or decompose vector on the x and y axis
θ
Hypotenuse (H)
Opposite (O
)
Adjacent (A)
θ
x
y
r
rx
ry
sinrry cosrrx
I Quadrantx +, y+sin +, cos +, tan +0<ϴ<900
IIx -, y+sin +, cos -, tan -900<ϴ<1800
IIIx -, y-sin -, cos -, tan +1800<ϴ<2700
IVx +, y -sin -, cos +, tan -2700<ϴ<3600
x
y1tan
1800 -α
1800 +α 3600 –α or -α
α
O=?
2
300
Ex1.O=?, H=?
400
3
A
O
O=?, A=?
Θ=?
2
1
θ=?, O=?
• Ex2.
Say you walk 3 m right and 11 m north, find the magnitude and direction of displacement.
• Ex3
θ O x
y
-2m
-1 m
r
r=?, θ=?
3-2 Adding and Subtracting Vectors
• Adding vectors Graphically
BAC
Connect vector head and tail, the sum vector is free tail to point free head
A
BC
BACD
A
B
CD
• Adding Vectors: parallelogram method
• Adding Vectors Using Component Cx=Ax+Bx
Cy=Ay+By
Ex1.
A=3, 200 ; B=5, 450 C=?
A
B
C
Ex2.
C=?
Ex3.
A=2 m, θ=250; B=3 m, θ=600
Find | | and θ
Ex4.
A= 3 m, θ=600, B=5 m , θ= - 1600
C
300
600
2
3
600
1600
200
A
B
• Subtracting Vectors
)( BABAD
Dx=Ax-Bx
Dy=Ax-By
Ex4.A= 10 m, 300; B=5 m, 600
Find , magnitude and direction ?
BAD