Dynamics
∆𝑑 = 𝑑2 − 𝑑1
∆𝑑
𝑣=
∆𝑡
∆𝑣
𝑎=
∆𝑡
𝑣𝑓 + 𝑣𝑖
∆𝑑 = (
) ∆𝑡
2
𝑣𝑓 = 𝑣𝑖 + 𝑎∆𝑡
∆𝑑 = 𝑣𝑖 ∆𝑡 + 1⁄2 𝑎∆𝑡 2
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎∆𝑑
∆𝑑 = 𝑣𝑓 ∆𝑡 − 1⁄2 𝑎∆𝑡 2
2𝑣𝑖 sin 𝜃
∆𝑡 =
𝑔
2
𝑣𝑖
∆𝑑𝑥 =
sin 2𝜃
𝑔
𝐹 = 𝑚𝑎
𝐹𝑠 = 𝜇𝑠 𝐹𝑁
𝐹𝐾 = 𝜇𝐾 𝐹𝑁
𝑣2
4𝜋 2 𝑟
𝑎𝑐 =
= 4𝜋 2 𝑟𝑓 2 = 2
𝑟
𝑇
𝑚𝑣 2
𝐹𝑐 =
𝑟
Energy and Momentum
𝑊 = 𝐹∆𝑑 cos 𝜃
𝐸𝐾 = 1⁄2 𝑚𝑣 2
𝑊 = ∆𝐸𝐾
1
1
𝑊 = 𝑚𝑣𝑓2 − 𝑚𝑣𝑖2
2
2
𝑊 = 𝑚𝑔∆𝑦
∆𝐸𝑔 = 𝑚𝑔∆𝑦
𝑊 ∆𝐸
𝑃=
=
𝑡
𝑡
𝐹𝑥 = −𝑘∆𝑥
𝐸𝑒 = 1⁄2 𝑘(∆𝑥)2
𝑚
𝑇 = 2𝜋√
𝑘
𝑝 = 𝑚𝑣
𝐹∆𝑡 = ∆𝑝
𝑚1 𝑣1 + 𝑚2 𝑣2 = 𝑚1 𝑣1′ + 𝑚2 𝑣2′
1
1
1
1
𝑚1 𝑣12 + 𝑚2 𝑣22 = 𝑚1 (𝑣1′ )2 + 𝑚2 (𝑣2′ )2
2
2
2
2
Gravitational, Electric, Magnetic Fields
𝐺𝑚1 𝑚2
𝐹𝐺 =
𝑟2
𝐺𝑚𝑝𝑙𝑎𝑛𝑒𝑡
𝑔=
𝑟2
𝐺𝑚
𝑣=√
𝑟
𝑘𝑞1 𝑞2
𝐹𝐸 =
= 𝑞𝜀
𝑟2
𝑘𝑞
𝜀= 2
𝑟
𝑊 = 𝐹𝐸 ∆𝑑
∆𝐸𝐸 = −𝑊
∆𝐸𝐸 = −𝑞𝜀∆𝑑
𝐸𝐸
𝑉=
𝑞
∆𝐸𝐸
∆𝑉 =
𝑞
−∆𝑉
𝜀=
∆𝑑
𝑊 = −𝑞∆𝑉
𝑘𝑞∆𝑑
𝑉= 2
𝑟
𝑘𝑞
𝑉=
𝑟
𝐹𝑀 = 𝑞𝑣𝐵 sin 𝜃
𝐹𝑜𝑛 𝑤𝑖𝑟𝑒 = 𝐼𝐿𝐵 sin 𝜃
𝑚𝑣
𝑟=
𝑞𝐵
Wave Nature of Light
𝑣 = 𝑓𝜆
𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
𝑐
𝑛=
𝑣
𝜆1
𝑛=
𝜆2
Δ𝑠𝑛 = |𝑃𝑛 𝑆1 − 𝑃𝑛 𝑆2 |
1
Δ𝑠𝑛 = (𝑛 − ) 𝜆
2
1 𝜆
sin 𝜃𝑛 = (𝑛 − )
2 𝑑
𝑥𝑛
sin 𝜃𝑛′ =
𝐿
1
𝑥𝑛 (𝑛 − 2) 𝜆
=
𝐿
𝑑
𝑑 sin 𝜃 = 𝑚𝜆
1
𝑑 sin 𝜃 = (𝑛 − ) 𝜆
2
𝑚𝐿𝜆
𝑥𝑚 =
𝑑
𝑐 = 𝜆𝑣𝑎𝑐 𝑓
𝑐
𝑛=
𝑣
2𝑡
𝑁=
𝜆𝑓𝑖𝑙𝑚
Both waves with phase change:
2𝑡 =
2𝑡 =
𝑛𝜆
𝑛𝑓𝑖𝑙𝑚
(constructive)
1
2
(𝑚+ )𝜆
𝑛𝑓𝑖𝑙𝑚
(destructive)
One of the waves with phase change:
2𝑡 =
2𝑡 =
1
2
(𝑚+ )𝜆
(constructive)
𝑛𝑓𝑖𝑙𝑚
𝑛𝜆
(destructive)
𝑛𝑓𝑖𝑙𝑚
𝑤
sin 𝜃𝑛
2
𝑤 sin 𝜃𝑛 = 𝜆 single-slit diffraction: first dark
fringes (destructive)
Δ𝐿 =
𝑤 = sin 𝜃2 = 2𝜆 single-slit diffraction:
second dark fringes
(destructive)
𝑤 sin 𝜃𝑛 = 𝑛𝜆 single-slit diffraction: nth dark
fringes (destructive)
3
𝑤 sin 𝜃 = 2 𝜆 single-slit diffraction: first bright
fringes (constructive)
1
𝑤 sin 𝜃𝑚 = (𝑚 + ) 𝜆 single-slit diffraction:
2
nth bright fringes
(constructive)
𝜆𝐿
∆𝑦 =
𝑤
𝜆 = 𝑤 sin 𝜃1
𝑚𝜆 = 𝑤 sin 𝜃𝑚
Modern Physics
∆𝑡𝑠
∆𝑡𝑚 =
2
√1 − 𝑣2
𝑐
𝐿𝑚 = 𝐿𝑠 √1 −
𝐸𝑡𝑜𝑡𝑎𝑙 =
𝑣2
𝑐2
𝑚𝑐 2
2
√1 − 𝑣 2
𝑐
𝐸𝑟𝑒𝑠𝑡 = 𝑚𝑐 2
𝐸𝐾 = 𝐸𝑡𝑜𝑡𝑎𝑙 − 𝐸𝑟𝑒𝑠𝑡
𝑊 = 𝑒∆𝑉
ℎ𝑐
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓 =
𝜆
𝐸𝐾 = ℎ𝑓 − 𝑊
ℎ𝑓 ℎ
𝑝𝑝ℎ𝑜𝑡𝑜𝑛 =
=
𝑐
𝜆
2.90 × 10−3 m ∙ K
𝜆𝑚𝑎𝑥 =
𝑇
ℎ
ℎ
𝜆= =
𝑝 𝑚𝑣
ℎ
Δ𝑥Δ𝑝 ≥
4𝜋