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PHYS*1300 FORMULA SHEET Energy & Momentum Kinematics & Dynamics

𝑣 = 𝑣0 + 𝑎𝑡 𝑥 = 𝑥0 + ½ ( 𝑣0 + 𝑣 )𝑡 𝑥 = 𝑥0 + 𝑣0 𝑡 + ½ 𝑎𝑡 2 2

𝑣 =

𝑣02

+ 2𝑎∆𝑥

2𝜋𝑟 𝑣= 𝑇 𝑎𝑐 =

𝑣2 4 𝜋2 𝑟 = 4𝜋 2 𝑟𝑓 2 = 𝑇2 𝑟 ∑ 𝐹 = 𝐹𝑅 = 𝑚𝑎

󰇍 𝐹 = 𝑞𝐸

𝑊 = 𝐹∆𝑟 𝑐𝑜𝑠 𝜃 = 𝐹𝑥 ∆𝑥 + 𝐹𝑦 ∆𝑦

𝑈 = 𝑞|𝐸󰇍|𝑦

𝑊𝑡𝑜𝑡 = ∆𝐸𝐾

𝑈=𝑞𝑉

𝑃=

𝐸 𝑡

1 𝐸𝐾 = 𝑚𝑣 2 2 𝐸𝑝 = 𝑚𝑔ℎ 𝐸𝑝1 + 𝐸𝑘1 = 𝐸𝑝2 + 𝐸𝑘2 𝑝 = 𝑚𝑣 󰇍󰇍󰇍󰇍 󰇍 = 𝑚Δ𝑣 󰇍󰇍󰇍󰇍 Δ𝑝

𝐹𝐾 = 𝜇𝑘 𝐹𝑁

󰇍󰇍󰇍󰇍󰇍 = 𝐹𝑅 ∆𝑡 ∆𝑝

𝐹𝐺 = 𝑚𝑔

|𝐹| =

𝐺𝑚1 𝑚2 𝑟2

𝑘|𝑞1 ||𝑞2 | 𝑟2

𝑊 = 𝐹 ∙ 𝑟

𝐹𝑠,𝑚𝑎𝑥 = 𝜇𝑠 𝐹𝑁

𝐺𝑀 𝑔= 2 𝑟

|𝐹| =

Δ𝑈 = 𝑞 Δ𝑉 = −Δ𝐸𝑘 |𝐸| 𝑦 𝑉 = 󰇍󰇍󰇍󰇍󰇍 𝑈=

𝑘𝑞1 𝑞2 𝑟

𝑉=

𝑉 = ∑ 𝑉𝑖 ∆𝑉 = 𝐼𝑅 𝑃 = ∆𝑉 𝐼 = 𝑅 𝐼 2 = 𝐼=

Electricity and Current 󰇍| = |𝐸

𝑘|𝑞| 𝑟2

𝑘𝑞2 𝑟

∆𝑉 2 𝑅

Δ𝑞 Δ𝑡

Series: 𝑅 = 𝑅1 + 𝑅2 + 𝑅3 + …

Parallel: 1 𝑅

=

1 + . .. 1 1 + 𝑅3 + 𝑅1 𝑅2

P = (V)I Waves and Acoustics 𝑣 = 𝜆𝑓 =

𝜆 𝜔 = 𝑇 𝑘 𝑘=

𝜔 = 2𝜋𝑓

,

𝑦 = 𝐴 sin (

2𝜋𝑡 2𝜋𝑥 ± ) 𝜆 𝑇

𝜆

= 𝐴 sin(𝜔𝑡 ± 𝑘𝑥 ) 𝐿=

𝑛𝜆 2

, 𝑓𝑛 = 𝑛

𝐿=

𝑛𝜆 4

, 𝑓𝑛 = 𝑛 4𝐿 for 𝑛 = 1,3,5,7, ..

𝑣

2𝐿

for 𝑛 = 1,2,3,4, ..

𝑣

𝑦 = ±2𝐴 cos(𝜔t) sin(𝑘𝑥) 𝐼=

𝑃 𝑃 (point source) = 4𝜋𝑟 2 𝐴 𝐸 = 𝑃𝑡 𝐼1 𝑟22 = 𝐼2 𝑟12 𝑓𝐵 = |𝑓2 − 𝑓1 |

0

where 𝐼0 = 10

−12

Wm

X

𝑁 = 𝑁0 𝑒 −μx 𝐴 = 𝐴0 𝑒 −λt 𝐴(𝑡) = λ ∙ 𝑁(𝑡) 𝑇1/2 =

ln 2 𝜆

𝑚𝑒𝑎𝑛 𝑓𝑟𝑒𝑒 𝑝𝑎𝑡ℎ = 𝜇 −1 ∆𝐸 = ∆𝑚𝑐 2 𝑅𝑜 = 1 × 10

𝑉𝑠𝑝ℎ𝑒𝑟𝑒 =

-2

Radioactivity 𝐴 𝑍

2𝜋

𝐴𝑠𝑝ℎ𝑒𝑟𝑒 = 4𝜋𝑟 2

𝐼 𝛽 = 10 log10 (𝐼 )

−12

𝑅 (𝑡) = 𝑅0 𝑒 −𝜆𝑡 ___________________________ Useful Information 𝐶 = 2𝜋𝑟 1 eV = 1.6 x 10 -19 J 1 u = 1.66054 x 10−27 kg

4 3 𝜋𝑟 3

𝜋 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 = 180o

𝑥=

−𝑏 ± √𝑏 2 − 4𝑎𝑐 2𝑎

𝑐 = 3.0 x 108 ms-1 𝑘 = 9.0 x 109 Nm2C-2 𝑁𝐴 = 6.02 x 1023 mol-1 ℎ = 6.63 x 10 -34 Js 𝑒 = 1.6 x 10 -19 C 𝑔 = 9.8 m/s2 𝐺 = 6.67 x 10-11 N m2/kg For sound in air: 𝑣 = 340 ms-1 For sound in water: 𝑣 = 1550 ms-1 Natural e = 2.718…. 𝑚𝑒 = 9.1 x 10 -31 kg 𝑚𝑝 = 1.673 x 10 -27 kg 𝑚𝑛 = 1.675 x 10 -27 kg Updated: F20...