chapter 1: interactions and motion
TRANSCRIPT
![Page 1: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/1.jpg)
⟨1, 0, 0⟩
⟨0, 0, 1⟩
⟨0, 1, 0⟩
x
z
y
![Page 2: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/2.jpg)
Hydrogen
1 electron
Carbon
6 electrons
Iron
26 electrons
Uranium
92 electrons
1 × 10 –10 m
Hydrogen nucleus
1 proton
Tritium nucleus
1 proton + 2 neutrons
Deuterium nucleus
1 proton + 1 neutron
Carbon nucleus
6 protons + 6 neutrons
Helium-3 nucleus
2 protons + 1 neutron
Helium-4 nucleus
2 protons + 2 neutrons
1 × 10–15 m
× −
× −
![Page 3: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/3.jpg)
Cluster
of galaxies
Galaxy
The planet
Jupiter in our
Solar System
![Page 4: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/4.jpg)
× −
+
+
+
+
+
+
+
+
+
+
× ×
+
+
+
+
+
+
+
++
××
![Page 5: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/5.jpg)
×
1 2
1
23
![Page 6: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/6.jpg)
![Page 7: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/7.jpg)
Push by hand
Push by table
Motion of box
![Page 8: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/8.jpg)
×
�
〈 〉
� = 〈 − 〉� = 〈− − 〉
![Page 9: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/9.jpg)
〈 〉
x
y
z
+ + +
x
z
y
ry = 3 m
rz = 2 m
rx = 4 m
r
� = 〈 〉 � = 〈 〉
� = 〈 〉� = 〈 〉� = 〈 〉
� = 〈 〉
=
=
=
�� = 〈− − 〉 −
![Page 10: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/10.jpg)
〈 〉 �
x
z
y
ry = 3 m
rz = 2 mrx = 4 m
b
� = 〈 〉〈 〉
x
y
〈− − 〉
〈− − 〉
− ◦
=
=− ◦
� �/|� |
ˆ
�+�
�−�
�/
� •��×�
![Page 11: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/11.jpg)
12
p
p
2p
–p
–2p
–3p
3p
� = 〈 〉 � = 〈 〉
� = 〈 〉 �=
⟨ ⟩
〈 − 〉= 〈 − 〉
− 〈 〉= 〈 − 〉
� = 〈 − 〉�/
x
z
y
ry = 3 m
rz = 2 m
rx = 4 m
r
x
y
z√(x2 + z2)
√(x2 + z2) + y2
〈 〉
√+ + =
√=
|� | �
|� |=
|� |
� = 〈 〉 |� |=√
+ +
![Page 12: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/12.jpg)
− �
|− � |= |− | · |� |
|− � |= |− | · |� |=√
+ +
� = 〈 − 〉∣∣∣∣− �
∣∣∣∣
ˆ
〈 〉〈 〉 √
+ + =〈 /
√/√
/√ 〉√(
√)
+
(√
)+
(√
)=
= 〈 〉j= 〈 〉ˆ = 〈 〉
k
x
z
y
j ˆ
〈 − 〉= + − j+ ˆ
ˆ = 〈 〉 ˆ= 〈 〉v = ⟨1.5, 1.5, 0⟩ m/s
v = ⟨ , 0⟩,√22
√22
ˆ�
� = |� | · ˆ
〈 〉= 〈 〉
![Page 13: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/13.jpg)
ˆ=�
|� | =〈 〉√+ +
ˆ=
⟨√
+ +√
+ +√
+ +
⟩
� = 〈− − 〉
|�|=√
− + + − =
ˆ =�
|�| =〈− − 〉
= 〈− − 〉� = 〈− − 〉
� = 〈 − 〉= 〈 − 〉·� = 〈 − 〉
= 〈 − 〉= 〈 − 〉
� =�
= = =
|� |= |� | ˆ =ˆ
r2
r1
� �� = 〈 − 〉
� =� ˆ �
� = 〈 〉 � = 〈 〉� + � = 〈 + + + 〉
〈 〉+ 〈− 〉= 〈− 〉� − � = 〈 − − − 〉
〈 〉−〈− 〉= 〈 − − 〉
![Page 14: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/14.jpg)
� = � + � � − � = �
� − � = � + −�
x
y
A + B
x
y
x
y
B
B
B
A
A
A
Ay
By
Ax Bx
� + �� �
�
� �
〈 〉 〈− 〉〈 〉+ 〈− 〉
� =〈 − 〉 � =〈 − 〉� + �
|� + � | |� |+ |� | |� + � | = |� |+ |� | � − �
|� − � | |� |− |� | |� − � |= |� |− |� |
�
� � = � +�
� �
��
� �
B
A
A − B� �
��
� �
� − � �
� � � − �
� + � − � = �
a2
a1
a1
a2 − a1
a2 + a1
a2
� =�−� � =�−� �+�=� �+�=� �+� =�
![Page 15: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/15.jpg)
� + � = � + �
r
t
s
� − � =/ � − �
� + � − � = � + � − �
Δ
Δ
Δ �
�
Δ� =� −�
Δ� � � −�Δ −
Δ
Δ = +Δ =−
–4 –2 0 2 4 6 m
–2
0
2
4
6 m
–4
r2 – r1r1
r2
� �
� =� −�
〈− 〉〈 〉 Δ�
Δ
x
|A| = 1
θx
A
Ax
String
+ θ +ˆ
![Page 16: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/16.jpg)
| ˆ |=
θ = = = θ
θ θ ◦
+ ˆ θ ◦
θ
+ ˆ
ˆ= 〈 θ θ θ 〉
θ +θ = ◦
θ = ◦−θ = θ θθ
θ = θ
〈 〉 + θ〈 〉
θ θ ≤ ◦
θ 〈 〉θ
θ ≤ ◦
θ 〈 〉θ
θ ≤ ◦
� 〈− 〉
ˆ=〈− 〉√
− + += 〈− 〉
ˆ= 〈 θ θ θ 〉 θ =−θ = ◦
θ = θ = ◦
θ = θ = ◦
θ = ◦ θ = ◦ ◦
◦
![Page 17: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/17.jpg)
◦
20°
〈 〉 +θ = ◦
〈 〉 +θ = ◦ +
θ = ◦
〈 ◦ ◦ ◦〉= 〈 〉
◦=
◦+
◦
× × −
× × −
× × −
× × −
![Page 18: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/18.jpg)
(��
�
)(���
)(��
)(�
��
)(���
)(��
��
)(��
)=
� |�|
= /
|� |= =
|� |= =
![Page 19: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/19.jpg)
Δ� = � −� ��
−
Star Comet
location B
Comet
location A
rf
ri
∆r = r f – r i
Δ�
� =� −�
−Δ
� =Δ�
Δ
=� = 〈 〉 =
� = 〈 〉
0 1 2 3 4 5 m
1
2
3
4
5 m
0
rf – ri
rf
ri
� � � −�� −�
� −� = 〈 〉 −〈 〉 = 〈 − 〉
� −�+ −
� −� −
� =� −�
− =〈 − 〉
− =〈 − 〉
= 〈 − 〉
![Page 20: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/20.jpg)
� −� − �
|� |=√
+ − + =
ˆ =�
|� | =〈 − 〉
= 〈 − 〉
√+ − + =
|�|ˆ = 〈 − 〉= 〈 − 〉�
0 1 2 3 4 5 m
1
2
3
4
5 m
0
vavg
rf – ri
rf
ri
〈 〉〈 〉
� −� =� −
![Page 21: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/21.jpg)
==
� −� = � −� −
� =� +� −
� =� +� Δ
� =� +� Δ
〈 〉= 〈 〉+ 〈 〉Δ
= + Δ
= + Δ
= + Δ
= � =〈 − 〉�=〈 − 〉 =
� = 〈 − 〉 + 〈 − 〉 −� = 〈 − 〉 + 〈 − 〉� = 〈 − 〉
〈 × ×− × 〉
![Page 22: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/22.jpg)
〈 〉〈 〉〈 〉〈 〉〈 〉〈 〉
A
B
CD
E
F
y
x
rDB rEB
rCB
Δ
� =Δ�
Δ=� −�
− =〈 〉−〈 〉
−= 〈 〉
� =Δ�
Δ=� −�
− =〈 〉−〈 〉
−= 〈 〉
� =Δ�
Δ=� −�
− =〈 〉−〈 〉
−= 〈 〉
B
C
D
vCB
vDB
vEB
vinstantaneous
�
��
![Page 23: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/23.jpg)
−Δ
5
4 2
1
3
Star
a
e
b
cg
d
h
f
j zero magnitude
Δ�/Δ Δ
� =Δ →
Δ�
Δ� =
�
Δ
� =�= 〈 〉=
⟨ ⟩= 〈 〉
�
�
�
× −
× −
� =〈 × − 〉
× − = 〈 × 〉
×
� = �/� = �/
![Page 24: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/24.jpg)
� =�
� =Δ�
Δ
+
� =Δ�
Δ=
〈 〉−〈 〉= 〈 〉
� = |�|ˆ
� =�=
|�|ˆ+ |�| ˆ
〈 +− 〉
==
〈 − 〉
〈 − 〉 �
![Page 25: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/25.jpg)
〈 − 〉�
〈 〉
�
� ≈ �
·Scalar Vector
pf = 0
pi
� = 〈 − 〉 = 〈 − 〉 ·
![Page 26: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/26.jpg)
� ·
Δ� = � −� = 〈 〉 · −〈 − 〉 ·= 〈− 〉 ·
|Δ� |=√
− + · = ·
� = 〈 − 〉 = 〈 − 〉 ·Δ� = 〈 〉 · −〈 − 〉 ·
= 〈− 〉 ·|Δ� |=
√− + · = ·
B
C D
E
pB
pCpD
pE
� =〈 〉 · � =〈 〉 ·
Δ� = � −� = 〈 〉 · −〈 〉 ·= 〈− − 〉 ·
Δ�
pC
pBp
Δ�
��
〈 〉
![Page 27: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/27.jpg)
� = 〈 〉 = 〈 〉 ·� = 〈− 〉 = 〈− 〉 ·Δ� = 〈− 〉 · −〈 〉 ·Δ� = 〈− 〉 ·
pf
pi
Δ|� |= |� |− |� |Δ|� |=
√− + + · −
√+ + ·
Δ|� |= ·
|Δ� |=√− + + = ·
Δ� |Δ� |Δ|� |
×
〈 − × 〉〈− × 〉
++ Δ�
Δ�
A
C
D
B
Mars
Sunx
z
pBpA
+ +
� ≈ �/
〈 〉 ·〈 〉
![Page 28: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/28.jpg)
� ≈ �=
〈 〉 ·= 〈 〉
� −� =�Δ
� =� −�Δ
= 〈 〉 − 〈 〉= 〈− − 〉
=〈 〉 〈 − 〉 ·
=
= × �
� = γ �
γ
γ = √−( |�|)
�� ×
· γ
γ
![Page 29: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/29.jpg)
× −
〈 × × − × 〉
|�|=√
× + × + − × = ×|�|
=×× =
γ = √− =
� = × − 〈 × × − × 〉� = 〈 × − × − − × − 〉 ·
|� |=√
× − + × − + − × − ·|� |= × − ·
γv| | m/s v| |/c
2.9997 × 108
0
3
3 × 108
3 × 106
3 × 107
300
2.997 × 108
1.5 × 108
0.9999
0
1 × 10−8
1
0.01
0.1
1 × 10−6
0.999
0.5
Infinite!
Impossible!
70.7124
1.0000
1.0000
1.0001
1.0050
1.0000
22.3663
1.1547
γγ
γ =
γ ≈ γ
� ≈ · �
γ
γ = √−( |�|)
0 0.5 1.0
0
10
20
20
1
γ
c
γ
v
γ |�|/γ
|�| ≈ γ
|�|/ − |�|/ ≈ − ≈ γ ≈
|�| � γ ≈� ≈ · � ≈ �
|�|/ γ|�|/ =
|�|= × γ
× γ� ≈ �
� = γ �
γγ
![Page 30: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/30.jpg)
γ
×
�≈ �
γ
γ γ≈
� ≈ �/� = γ �
�
� =�/√+
( |� |)
![Page 31: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/31.jpg)
〈 × − 〉 ·
= = × −
� =�/√+
( |� |) =〈 × − 〉 ·
× −
√+
( × − ·× − ×
)= 〈 × 〉
� =� +� Δ
= 〈 〉 + 〈 × 〉 × −
= 〈 〉
〈 − × 〉
![Page 32: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/32.jpg)
〈− − 〉
〈 〉
+ + +
〈− − 〉
Δ =
� =� +�Δ
Δ
![Page 33: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/33.jpg)
× −
![Page 34: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/34.jpg)
![Page 35: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/35.jpg)
x
y
y
x
◦
◦
v2 = 0
c = 3 108 m/s
c = 3 108 m/s
c = 3 108 m/s
v3
v1
= ×
= ×
![Page 36: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/36.jpg)
γγ
γ ≈
×
×× ×
� � ≈ � � ≈ �/
� �
|� |= √− |�|/ |�|
|� |=
|�|− |�|/
− |�|/ |� | −( |� | )
|�| = |�|(+
|� | )|�| =
|� |
|�|= |� |/√+
( |� |)
� ��
� = |� |ˆ � = |�|ˆ
� � ˆ = ˆ
� = |�|ˆ =|� |/√+
( |� |) ˆ =|� |ˆ /√+
( |� |)
� =�/√+
( |� |)
![Page 37: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/37.jpg)
� =� + √+
( |� |)(�)Δ Δ
|� | ≈ |�|√+
( |�|) ≈
� =� + �/ Δ
〈 〉�
ˆ=�/|� |� = |� | ˆ
ˆ= 〈 θ θ θ 〉
ΔΔ Δ = −
Δ� =� −�Δ
� =Δ�
Δ=� −�
−
�
� =� +� Δ
� =Δ →
Δ�
Δ=
�
� =�/√+
( |� |) � ≈ �/
� =�/
![Page 38: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/38.jpg)
� = γ �
γ = √− |�|/
� = √− |�|/
�
� ≈ � |�| �
≈ × −
≈ × −
×
γγ
γ γγ
γγ ≈
××
D FE
A
B
C
![Page 39: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/39.jpg)
×
�/ |� |/〈 〉 ·�
� �
d
b
f
c
e
g
a
� �=〈 ×− × 〉
c g
a
��
� = �
� � =−�
�
� =−�
x
y
c
a d
b
〈 〉 � = 〈− 〉� 〈− 〉
−� −��
� = 〈 − 〉 =
� � = −� �� 〈− − 〉
−�〈− − − 〉
x
z
y
2 m
3 m6 m
d
〈 〉〈 〉
� =〈− 〉 〈− 〉
� �
〈− − 〉
� �
� �
![Page 40: Chapter 1: Interactions and Motion](https://reader034.vdocuments.net/reader034/viewer/2022052308/586774561a28abb4408bb3ef/html5/thumbnails/40.jpg)
� �/〈− − 〉
�/�/ �
�/ �
�
� �
� = 〈 − 〉|�| ·ˆ
�=〈 〉� ˆ
� ˆ
〈 〉 ˆ �
|�| ˆ |�| ˆ
〈 × − − × − × − 〉�
|� | ˆ�
��
–4 –2 0 2 4 6 m
–2
0
2 m
–4
r1
r2
〈 〉〈 − 〉
〈 〉〈− 〉
〈 × × × 〉〈− × − × × 〉
〈− × × − × 〉〈 × − × × 〉 �
� ˆ�
〈 〉〈 〉
〈 〉
〈 − 〉〈− 〉 μ = × −
〈 − 〉 〈 − 〉
〈 〉〈 〉
〈 ◦ ◦〉〈 ◦ ◦〉
〈 〉 〈 〉
×〈− ×
− × × 〉
〈− × − × × 〉
�
〈− − 〉〈 − 〉
〈− − 〉
〈− 〉 〈− 〉 〈 〉
= 〈 〉〈 − 〉 =
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〈 − 〉 μ〈 − 〉
× −
μ
〈 − 〉〈− 〉
+〈 〉
〈 〉
〈 〉〈 〉〈 〉
==
A
B
C D
E
F
x
y
〈 − 〉
〈 − 〉
〈 − 〉 |� |·
� = 〈 − 〉 ·|� |
〈 〉 ·
〈 〉〈− 〉
−
Δ�
◦
◦Δ�
|Δ� | ◦◦
B
C D
E
pB
pCpD
pE
� = 〈 〉 ·� = 〈 〉 ·� = 〈 − 〉 ·
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� = 〈 − 〉 ·� = 〈 − 〉 ·
Δ�
〈 − 〉 ·〈 〉
〈 〉 ·
〈 − 〉 ·〈 − 〉
〈 ×− × 〉 〈 × − × 〉 ·
|� |/ =|� |
γ γ ��
γ|� |/ =
|�|= = ×
ˆ = 〈 − − 〉× − γ
|�|/ =
� = |�|ˆ|� |/ |�|
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Δ
+
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〈 − 〉
〈 − 〉〈 − − 〉 〈
− 〉
〈 〉〈− 〉 〈− 〉
× −〈 − 〉 〈 − 〉
〈 × × − × 〉
〈 − 〉〈 − 〉 〈 〉 〈 〉
〈− × − × 〉 ·
Δ�
〈 〉〈 − × − 〉 · × − ·