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Dynamics
βˆ†π‘‘ = 𝑑2 − 𝑑1
βˆ†π‘‘
𝑣=
βˆ†π‘‘
βˆ†π‘£
π‘Ž=
βˆ†π‘‘
𝑣𝑓 + 𝑣𝑖
βˆ†π‘‘ = (
) βˆ†π‘‘
2
𝑣𝑓 = 𝑣𝑖 + π‘Žβˆ†π‘‘
βˆ†π‘‘ = 𝑣𝑖 βˆ†π‘‘ + 1⁄2 π‘Žβˆ†π‘‘ 2
𝑣𝑓2 = 𝑣𝑖2 + 2π‘Žβˆ†π‘‘
βˆ†π‘‘ = 𝑣𝑓 βˆ†π‘‘ − 1⁄2 π‘Žβˆ†π‘‘ 2
2𝑣𝑖 sin πœƒ
βˆ†π‘‘ =
𝑔
2
𝑣𝑖
βˆ†π‘‘π‘₯ =
sin 2πœƒ
𝑔
𝐹 = π‘šπ‘Ž
𝐹𝑠 = πœ‡π‘  𝐹𝑁
𝐹𝐾 = πœ‡πΎ 𝐹𝑁
𝑣2
4πœ‹ 2 π‘Ÿ
π‘Žπ‘ =
= 4πœ‹ 2 π‘Ÿπ‘“ 2 = 2
π‘Ÿ
𝑇
π‘šπ‘£ 2
𝐹𝑐 =
π‘Ÿ
Energy and Momentum
π‘Š = πΉβˆ†π‘‘ cos πœƒ
𝐸𝐾 = 1⁄2 π‘šπ‘£ 2
π‘Š = βˆ†πΈπΎ
1
1
π‘Š = π‘šπ‘£π‘“2 − π‘šπ‘£π‘–2
2
2
π‘Š = π‘šπ‘”βˆ†π‘¦
βˆ†πΈπ‘” = π‘šπ‘”βˆ†π‘¦
π‘Š βˆ†πΈ
𝑃=
=
𝑑
𝑑
𝐹π‘₯ = −π‘˜βˆ†π‘₯
𝐸𝑒 = 1⁄2 π‘˜(βˆ†π‘₯)2
π‘š
𝑇 = 2πœ‹√
π‘˜
𝑝 = π‘šπ‘£
πΉβˆ†π‘‘ = βˆ†π‘
π‘š1 𝑣1 + π‘š2 𝑣2 = π‘š1 𝑣1′ + π‘š2 𝑣2′
1
1
1
1
π‘š1 𝑣12 + π‘š2 𝑣22 = π‘š1 (𝑣1′ )2 + π‘š2 (𝑣2′ )2
2
2
2
2
Gravitational, Electric, Magnetic Fields
πΊπ‘š1 π‘š2
𝐹𝐺 =
π‘Ÿ2
πΊπ‘šπ‘π‘™π‘Žπ‘›π‘’π‘‘
𝑔=
π‘Ÿ2
πΊπ‘š
𝑣=√
π‘Ÿ
π‘˜π‘ž1 π‘ž2
𝐹𝐸 =
= π‘žπœ€
π‘Ÿ2
π‘˜π‘ž
πœ€= 2
π‘Ÿ
π‘Š = 𝐹𝐸 βˆ†π‘‘
βˆ†πΈπΈ = −π‘Š
βˆ†πΈπΈ = −π‘žπœ€βˆ†π‘‘
𝐸𝐸
𝑉=
π‘ž
βˆ†πΈπΈ
βˆ†π‘‰ =
π‘ž
−βˆ†π‘‰
πœ€=
βˆ†π‘‘
π‘Š = −π‘žβˆ†π‘‰
π‘˜π‘žβˆ†π‘‘
𝑉= 2
π‘Ÿ
π‘˜π‘ž
𝑉=
π‘Ÿ
𝐹𝑀 = π‘žπ‘£π΅ sin πœƒ
πΉπ‘œπ‘› π‘€π‘–π‘Ÿπ‘’ = 𝐼𝐿𝐡 sin πœƒ
π‘šπ‘£
π‘Ÿ=
π‘žπ΅
Wave Nature of Light
𝑣 = π‘“πœ†
𝑛1 sin πœƒ1 = 𝑛2 sin πœƒ2
𝑐
𝑛=
𝑣
πœ†1
𝑛=
πœ†2
Δ𝑠𝑛 = |𝑃𝑛 𝑆1 − 𝑃𝑛 𝑆2 |
1
Δ𝑠𝑛 = (𝑛 − ) πœ†
2
1 πœ†
sin πœƒπ‘› = (𝑛 − )
2 𝑑
π‘₯𝑛
sin πœƒπ‘›′ =
𝐿
1
π‘₯𝑛 (𝑛 − 2) πœ†
=
𝐿
𝑑
𝑑 sin πœƒ = π‘šπœ†
1
𝑑 sin πœƒ = (𝑛 − ) πœ†
2
π‘šπΏπœ†
π‘₯π‘š =
𝑑
𝑐 = πœ†π‘£π‘Žπ‘ 𝑓
𝑐
𝑛=
𝑣
2𝑑
𝑁=
πœ†π‘“π‘–π‘™π‘š
Both waves with phase change:
2𝑑 =
2𝑑 =
π‘›πœ†
π‘›π‘“π‘–π‘™π‘š
(constructive)
1
2
(π‘š+ )πœ†
π‘›π‘“π‘–π‘™π‘š
(destructive)
One of the waves with phase change:
2𝑑 =
2𝑑 =
1
2
(π‘š+ )πœ†
(constructive)
π‘›π‘“π‘–π‘™π‘š
π‘›πœ†
(destructive)
π‘›π‘“π‘–π‘™π‘š
𝑀
sin πœƒπ‘›
2
𝑀 sin πœƒπ‘› = πœ† single-slit diffraction: first dark
fringes (destructive)
Δ𝐿 =
𝑀 = sin πœƒ2 = 2πœ† single-slit diffraction:
second dark fringes
(destructive)
𝑀 sin πœƒπ‘› = π‘›πœ† single-slit diffraction: nth dark
fringes (destructive)
3
𝑀 sin πœƒ = 2 πœ† single-slit diffraction: first bright
fringes (constructive)
1
𝑀 sin πœƒπ‘š = (π‘š + ) πœ† single-slit diffraction:
2
nth bright fringes
(constructive)
πœ†πΏ
βˆ†π‘¦ =
𝑀
πœ† = 𝑀 sin πœƒ1
π‘šπœ† = 𝑀 sin πœƒπ‘š
Modern Physics
βˆ†π‘‘π‘ 
βˆ†π‘‘π‘š =
2
√1 − 𝑣2
𝑐
πΏπ‘š = 𝐿𝑠 √1 −
πΈπ‘‘π‘œπ‘‘π‘Žπ‘™ =
𝑣2
𝑐2
π‘šπ‘ 2
2
√1 − 𝑣 2
𝑐
πΈπ‘Ÿπ‘’π‘ π‘‘ = π‘šπ‘ 2
𝐸𝐾 = πΈπ‘‘π‘œπ‘‘π‘Žπ‘™ − πΈπ‘Ÿπ‘’π‘ π‘‘
π‘Š = π‘’βˆ†π‘‰
β„Žπ‘
πΈπ‘β„Žπ‘œπ‘‘π‘œπ‘› = β„Žπ‘“ =
πœ†
𝐸𝐾 = β„Žπ‘“ − π‘Š
β„Žπ‘“ β„Ž
π‘π‘β„Žπ‘œπ‘‘π‘œπ‘› =
=
𝑐
πœ†
2.90 × 10−3 m βˆ™ K
πœ†π‘šπ‘Žπ‘₯ =
𝑇
β„Ž
β„Ž
πœ†= =
𝑝 π‘šπ‘£
β„Ž
Δπ‘₯Δ𝑝 ≥
4πœ‹
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