Formelsammlung Physik PDF

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Kinematik Geradlinige Bewegung v = Konstant 𝑠 = 𝑣⋅𝑡 𝑠 = 𝑚 = Weg 𝑚 𝑠 𝑣 = 𝑠 = Geschwindigkeit 𝑣=𝑡 𝑠 𝑡 = 𝑠 = Zeit 𝑡=

Schräger Wurf

𝑣

Beschleunigte Bewegung 𝑚 𝑣 = 𝑎 ⋅𝑡 𝑎 = 𝑠2 = Beschleunigung 𝑣 𝑚 𝑎=𝑡 𝑣 = 𝑠 = Geschwindigkeit 𝑣 𝑡= 𝑡 = 𝑠 = Zeit 𝑎 𝑎 = 𝑠2 = Beschleunigung 𝑠 = 𝑚 = Weg 𝑡 = 𝑠 = Zeit

𝑠 = 2 ⋅ 𝑎 ⋅ 𝑡2 𝑎= 𝑡=

𝑚

1

2⋅𝑠 𝑡2

2⋅𝑠 √ 𝑎

Beschleunigte Bewegung mit Anfangsgeschwindigkeit 𝑚 𝑣 = 𝑣0 + 𝑎 ⋅ 𝑡 𝑣0 = 𝑠 = Anfangsgesch. 𝑚 𝑣0 = 𝑣 − 𝑎 ⋅ 𝑡 𝑎 = 𝑠2 = Beschleunigung 𝑣−𝑣0 𝑚 𝑡= 𝑣 = 𝑠 = Geschwindigkeit 𝑎 𝑣−𝑣 𝑎= 𝑡0 𝑡 = 𝑠 = Zeit

𝑠0 = 𝑚 = Anfangsweg 𝑚 𝑣0 = 𝑠 = Anfangsgesch. 𝑚 𝑎 = 𝑠2 = Beschleunigung 𝑚 𝑣 = 𝑠 = Geschwindigkeit 𝑡 = 𝑠 = Zeit

𝑠 = 𝑠0 + 𝑣0 ⋅ 𝑡 + 2 ⋅ 𝑎 ⋅ 𝑡 2 𝑎=

𝑡=

1

2⋅(𝑠−𝑠0 −𝑣0⋅𝑡) 𝑡2

−𝑣0 ±√𝑣02 −4⋅0,5⋅𝑎⋅(𝑠0 −𝑠) 𝑎

𝑠0 = 𝑠 − 𝑣0 ⋅ 𝑡 − 2 ⋅ 𝑎 ⋅ 𝑡 2 𝑣0 =

1

𝑠−𝑠0 −0,5⋅𝑎⋅𝑡2 𝑡

𝑣 2 − 𝑣02 = 2 ⋅ 𝑎 ⋅ 𝑠

𝑣 = 𝑠 = Geschwindigkeit 𝑚 𝑣0 = 𝑠 = Anfangsgesch. 𝑚 𝑎 = 𝑠2 = Beschleunigung 𝑠 = 𝑚 = Weg

𝑣 = √2 ⋅ 𝑎 ⋅ 𝑠 + 𝑣02

𝑣0 = √𝑣 2 − 2 ⋅ 𝑎 ⋅ 𝑠

𝑚

Durchschnittsgeschwindigkeit & -beschleunigung 𝑥 −𝑥 𝑚 𝑣 = 𝑡 1−𝑡 2 𝑣 = 𝑠 = Bahngeschwindigkeit 1 2 𝑚 𝑎 = 𝑠2 = Durchschnittsbeschleunigung 𝑡1 & 𝑡2 = 𝑠 = Zeitpunkte 𝑣 −𝑣 𝑎= 1 2 𝑡1 −𝑡2 𝑣1 & 𝑣2 = 𝑚𝑠 = Geschwindigkeit 𝑥1 & 𝑥2 = 𝑚 = zurückgelegter Weg Freier Fall 𝑚 𝑚 1 𝑔 = 𝑠2 = Fallbeschleunigung = 9,807 2 ℎ = 2 ⋅ 𝑔 ⋅ 𝑡2 𝑠 2⋅ℎ ℎ = 𝑚 = Fallhöhe 𝑔= 2 𝑡 𝑡 = 𝑠 = Zeit 𝑚 2⋅ℎ 𝑣 = 𝑠 = Geschwindigkeit 𝑡=√ 𝑔 𝑣 = √2 ⋅ ℎ ⋅ 𝑔

ℎ= 2⋅𝑔 Senkrechter Wurf nach oben 𝑣2

𝑣𝑎𝑏𝑤𝑢𝑟𝑓 = 𝑣𝑎𝑛𝑘𝑢𝑛𝑓𝑡

ℎ0 = 𝑚 = Abwurfhöhe 𝑚 𝑣0 = 𝑠 = Anfangsgesch. 𝑚 𝑔 = 𝑠2 = Fallbeschleunigung 𝑡 = 𝑠 = Zeit ℎ = 𝑚 = Höhe

ℎ = ℎ0 + 𝑣0 ⋅ 𝑡 − 2 ⋅ 𝑔 ⋅ 𝑡 2 𝑔=− 𝑡=

2⋅(ℎ−ℎ0 −𝑣0⋅𝑡) 𝑡2

−𝑣0 ±√𝑣02 +4⋅0,5⋅𝑔⋅(ℎ0−ℎ) −𝑔

ℎ0 = ℎ − 𝑣0 ⋅ 𝑡

𝑣 = 𝑣0 − 𝑔 ⋅ 𝑡 𝑣0 = 𝑣 + 𝑔 ⋅ 𝑡 𝑣 −𝑣 𝑡 = 0𝑔 𝑔=

1

𝑣0−𝑣 𝑡

𝑡𝑠𝑡𝑒𝑖𝑔. = √

1 +2

⋅ 𝑔 ⋅ 𝑡2

𝑚

𝑡𝑘𝑜𝑚𝑝. = √

2⋅ℎ 𝑔

𝑣0 = 𝑠 = Anfangsgesch. 𝑚 𝑔 = 𝑠2 = Fallbeschleunigung 𝑡 = 𝑠 = Zeit 𝑚 𝑣 = 𝑠 = Geschwindigkeit

8⋅ℎ 𝑔

2

𝑦=

1 −2

⋅𝑔⋅

𝑥 (𝑣 ) 𝑥

𝑣𝑔𝑒𝑠 = √𝑣𝑥2 + 𝑣𝑦2

𝑡=√

2⋅ℎ 𝑔

𝑥𝑤𝑒𝑖𝑡 = 𝑣𝑥 ⋅

𝑡𝑎𝑛 𝛼 = 𝑣𝑦 𝑣

𝑥

2

2⋅ℎ √ 𝑔

=−

𝑔

2⋅𝑣𝑥2

⋅𝑥

2

Δ𝑦 ! Δ𝑡

𝑣0⋅cos(𝜑)⋅𝑡 ) −21⋅𝑔⋅𝑡2 +𝑣0 ⋅sin(𝜑)⋅𝑡+𝑦0

𝑦(𝑡)

=0 → 𝑇𝑆 = 𝑣0⋅sin𝑔

𝑐1 = 2⋅𝑦02⋅𝑔 !

𝑣0

(𝜑)

𝑥(𝑇𝑆 ) =

𝑦(𝑡)=0

→𝑇 =

𝑐2 =

𝑣02

𝑔 sin(2⋅𝜑) 𝑐2 ⋅ 2 sin(𝜑)2 +𝑐1

𝑣0 sin(𝜑)+√sin(𝜑)2 +𝑐1 𝑔

𝑥(𝑇) = 𝑅 = 𝑐2 ⋅ cos(𝜑) ⋅ [sin(𝜑) + √sin2(𝜑) + 𝑐1 ] 𝜕𝑅

𝜕𝜑

! =0 → 𝜑𝑜𝑝𝑡 = arccos √𝑐1𝑐+1 1 +2

𝑅𝑜𝑝𝑡 = 𝑐2 ⋅ √𝑐1 + 1 tan(𝛽) =

𝑔⋅𝑡−𝑣0⋅cos(𝜑 ) 𝑣0⋅sin(𝜑)

𝑣0𝑚𝑖𝑛 = √𝑔 ⋅ √√𝑦02 + 𝑅2 − 𝑦0

𝑦 = Zeitfreie Darstellung

𝑣𝑔𝑒𝑠 = Gesamtgesch. 𝑡 = Fallzeit 𝑥𝑤𝑒𝑖𝑡 = Wurfweite 𝑡𝑎𝑛 𝛼 = Auftreffwinkel

Bewegungsgleichung Scheitel- Zeitpunkt Konstanten Scheitelpunkt Wurfzeit Wurfweite

Optimaler Abwurfwinkel Wurfweite unter optimalem Abwurfwinkel Aufprallwinkel Optimal Bedingungen bei vorgegebener Wurfweite und Abwurfhöhe

𝑦0 +√𝑦02+𝑅2

𝜑𝑜𝑝𝑡 = arccos √

2⋅√𝑦02 +𝑅2

𝑥 tan(𝜑) ⋅ 𝑥 + 𝑦0 𝑦(𝑥) = − 2⋅𝑣2⋅cos(𝜑) 2

𝐹 =𝑚⋅𝑎

Kraft

0

2

𝑚= 𝑎 𝐹 𝑎= 𝐹

𝑚

𝑝=𝑚⋅𝑣

Impuls 𝑚= 𝑣 𝑝 𝑣=𝑚 𝑝

Drehimpuls 𝐿 = 𝐽⋅𝜔 𝐽=

𝜔=

𝐿

𝜔 𝐿 𝐽

Potenzielle Energie 𝐸𝑃𝑜𝑡 = 𝑚 ⋅ 𝑔 ⋅ ℎ 𝑚= ℎ=

𝐸𝑃𝑜𝑡

𝑔⋅ℎ 𝐸𝑃𝑜𝑡 𝑔⋅𝑚

Kinetische Energie 𝐸𝑘𝑖𝑛 = 12 ⋅ 𝑚 ⋅ 𝑣 2

Rotations Energie

Waagerechter Wurf 2 Bewegungen erst Fallzeit dann die Weite ermitteln Bewegung in x-Richtung 𝑥 = 𝑣𝑥 ⋅ 𝑡 1 Bewegung in y- Richtung 𝑦 = ℎ − ⋅ 𝑔 ⋅ 𝑡2 𝑣𝑦 = 𝑔 ⋅ 𝑡

𝑥(𝑡) = (𝑥(𝑡)) = (

𝐸𝑟𝑜𝑡 = 12 ⋅ 𝐽 ⋅ 𝜔2

Mechanische Energie 𝑃=

𝐸 𝑡

Elastischer Stoß 𝑣1′ = 𝑣1 ⋅

(𝑚1−𝑚2)+2⋅𝑚2⋅𝑣2

𝑣2′ = 𝑣2⋅

𝑚1 +𝑚2

(𝑚2−𝑚1 )+2⋅𝑚1⋅𝑣1 𝑚1+𝑚2

Zeitunabhängige Bewegungsgleichung 𝐹 = 𝑁 = Kraft 𝑚 𝑎 = 𝑠2 = Beschleunigung 𝑚 = 𝐾𝑔 = Masse

𝑝 = 𝑁𝑠 = Impuls 𝑚 𝑣 = 𝑠 = Geschwindigkeit 𝑚 = 𝐾𝑔 = Masse

𝐿 = 𝑠 = Drehimpuls 𝐽 = 𝐾𝑔 ⋅ 𝑚² = Trägheitsmoment 𝑅𝑎𝑑 𝜔 = 𝑠 = Winkelgeschwindigkeit 𝐾𝑔 ⋅ 𝑚²

𝐸 = 𝐽 𝑜𝑢𝑙𝑒 = Energie Nm=Ws 𝑚 𝑚 𝑔 = 𝑠2 = Fallbeschleunigung = 9,807 2 𝑠 ℎ = 𝑚 = Fallhöhe 𝑚 = 𝐾𝑔 = Kilogramm

𝐸 = 𝐽 𝑜𝑢𝑙𝑒 = Energie Nm=Ws 𝑚 𝑣 = 𝑠 = Geschwindigkeit 𝑚 = 𝐾𝑔 = Kilogramm

𝐸 = 𝐽 𝑜𝑢𝑙𝑒 = Energie Nm=Ws 𝐽 = 𝐾𝑔 ⋅ 𝑚² = Trägheitsmoment 𝑅𝑎𝑑 𝜔 = 𝑠 = Winkelgeschwindigkeit 𝐸 = 𝐽 𝑜𝑢𝑙𝑒 = Energie Nm=Ws P= 𝑠𝐽 = Leistung Watt 𝑡 = 𝑠 = Zeit 𝑣1′ &𝑣2′ = 𝑚𝑠 = Ges. nach Stoß 𝑣1 &𝑣2 = 𝑚𝑠 = Ges. vor Stoß 𝑚1 &𝑚2 = 𝐾𝑔 = Masse

Unelastischer Stoß ′

′

Massenträgheitsmoment 𝑣1′ &𝑣2′ = 𝑚 = Ges. nach Stoß 𝑚 𝑠 𝑣1 &𝑣2 = = Ges. vor Stoß 𝐸 =1 𝐽 2 𝑠𝐾 & Masse

𝑣1 ⋅𝑚 𝑚11+𝑣 +𝑚22⋅𝑚2

′

𝑣 = 𝜔⋅𝑟

𝑟 = 𝑚 = Radius 𝑚 𝑣 = = Bahngeschwindigkeit 𝑠 1 𝜔 = 𝑠 = Winkelgeschwindigkeit

Bahngeschwindigkeit 𝜔= 𝑟 𝑣 𝑟= 𝜔 Winkelgeschwindigkeit 𝜔= 2⋅𝜋 ⋅𝑓 𝜔 𝑓= 𝑣

𝜋 = 3,1416 1 𝑓 = 𝑠 = ℎ𝑧 = Frequenz in Hertz

2⋅𝜋

2⋅𝜋 𝜔 = 𝑠 = Winkelgeschwindigkeit 𝜔= 𝑇 2⋅𝜋 𝑇 = 𝑠 = Zeit für eine Umdrehung 𝑇= 𝜔 Frequenz – Periodendauer

𝑓=

𝑇= 𝑓=

1

𝑓 = = ℎ𝑧 = Frequenz in Hertz 𝑇 = 𝑠 = Periodendauer

1

1 𝑠

𝑇 1

𝑓

𝑓 = 𝑠 = ℎ𝑧 = Frequenz in Hertz 𝑛 = Perioden-Umdrehungen 𝑡 = 𝑠 = Zeit

𝑛 𝑡

1

𝑣 𝑠 𝑎 𝑚

Translation Geschwindigkeit Weg Beschleunigung Masse Ekin

1 ⋅𝑚⋅𝑣2 2

𝑝 = 𝑚 ⋅ 𝑣

Impuls

𝐽 = 𝐾𝑔 ⋅ 𝑚2 = Trägheitmoment 1 𝜔=𝑠 = Winkelgeschwindigkeit

Rotation 𝜔 𝜑 𝛼 𝐽 1 ⋅𝐽⋅𝜔2 2

𝐿 = 𝐽 ⋅ 𝜔󰇍󰇍

Winkelgeschwindigkeit Winkel Winkelbeschleunigung Trägheitsmoment Erot Drehimpuls

𝑟1 = 106 𝐾𝑚 𝑟2 = 20 𝐾𝑚 1 𝑈𝑚𝑑𝑟𝑒ℎ𝑢𝑛𝑔 𝑛1 =

Drehimpulserhaltung Pulsar (𝐿1 = 𝐿2 ) → 𝜔2 = 𝑟12 ⋅ 𝜔1 𝑓=

2

𝑟2

𝜔2

2⋅𝜋

30 𝑇𝑎𝑔𝑒

Zentripetalbeschleunigung 𝑎𝑧 = 𝜔 2 ⋅ 𝑟 𝑟 = 𝑚 = Radius 𝑚 𝑎𝑧 = 𝑠2 = Zentripetalbeschleunigung 𝜔 = 𝑠 = Winkelgeschwindigkeit 1

Gravitationsgesetz 𝑚 ⋅𝑚 2 𝐹 =𝐺⋅ 122 = Gravitationskonstante 6,6724E-11 𝐺 = 𝑁𝑚 𝑣 𝐾𝑔2 𝑟 𝜔3 = 𝑟3 𝑚1 &𝑚2 = 𝐾𝑔 = Masse 𝐿3 = 𝑚3 ⋅ 𝑟 2 ⋅ 𝜔3 𝑟 = 𝑚 = Abstand der Massen 𝐿 𝐾𝑔⋅𝑚 𝜔12 = (𝑚 +𝑚3 )⋅𝑟2 𝐹 = 𝑠2 = 𝑁 = Newton 1 2 𝜔12 𝑓12 = Impulserhaltungssatz 2⋅𝜋 1 𝑝1 + 𝑝2 = 𝑝1′ + 𝑝2′ 𝑣1′ &𝑣2′ = 𝑚𝑠 = Ges. von m𝑛nachher = 𝑓12 ⋅ 60 𝑚𝑖𝑛 𝑚 𝑚1 ⋅ 𝑣1 + 𝑚2 ⋅ 𝑣2 = 𝑚1 ⋅ 𝑣1′ + 𝑚2 ⋅ 𝑣2′ = Ges. von m vorher 𝑣1 &𝑣2 = 𝑠 Drehmoment 󰇍󰇍 = 𝑟 × 𝐹 󰇍 = 𝑁𝑚 = Drehmoment 𝑚1 &𝑚2 = 𝐾𝑔 = Masse 𝑀 𝑀 Zentralelastischer Stoß 󰇍󰇍  𝑀 = 𝐽 ⋅ 𝛼

𝑟 = 1𝑚 𝑚1 = 𝑚2 = 2𝐾𝑔 𝑚3 = 0, 02𝐾𝑔 𝑚 𝑣3 = 100 𝑠

𝑛 = 𝑚𝑖𝑛 = Drehzahl 1

Jojo

ℎ1 = 6𝑚 𝑚1 = 25𝐾𝑔 𝑚2 = 125𝐾𝑔 ℎ2 =?

𝑣1 = √2 ⋅ 𝑔 ⋅ ℎ1 𝑣2′

=

ℎ2 =

𝑣2⋅(𝑚2−𝑚1 )+2⋅𝑚1⋅𝑣1 𝑚1+𝑚2 2

𝑣2′ 2⋅𝑔

Unelastischer Stoß

𝑎=

𝑣=(

𝐿 = 2𝑚 𝑚1 = 0, 02𝐾𝑔 𝑚2 = 2𝐾𝑔 ℎ =? 𝑣1 =?

(𝑣1′ = 𝑣2′) → 𝑣′ √2⋅𝑔⋅𝐻 𝑣1 = 𝑣 ⋅(𝑚1 −𝑚2 ′

𝑚1

)

𝑠 = 2⋅( 1

𝑎=(

𝑔⋅(𝑚2 −𝜇𝐺𝑅⋅𝑚1) ) 𝑡2 𝑚1+𝑚2

𝑔⋅(𝑚2 −𝜇𝐺𝑅⋅𝑚1) 𝑚1+𝑚2

𝑠 = 2⋅( 1

)

+ 𝑣0 ⋅ 𝑡 + 𝑠0

𝑚1 ⋅𝑔⋅(𝑚𝑚2 −𝜇𝐺𝑅⋅cos(𝛼)−sin(𝛼)) 1

𝑚1 +𝑚2

+ 𝑣0 ⋅ 𝑡 𝑚 𝑚1 ⋅𝑔⋅( 𝑚2 −𝜇𝐺𝑅⋅cos(𝛼)−sin(𝛼))

𝑎=(

1

𝑚1+𝑚2

) 𝑡2

+ 𝑠0 )

𝑎 = 𝑠2 = Beschleunigung 𝑠 = 𝑚 = Weg 𝑚

𝑚⋅𝑔

1 1

𝛼=𝑟⋅( 1

2

𝑚⋅𝑔

𝑔

2

1+12⋅𝑅 2 𝑟

) ⋅ 𝑡 + 𝑣0 𝑅2

𝑚+12⋅𝑚⋅ 2 𝑟

𝜔=𝑟⋅( 1

=

𝑟2

𝜑 =𝑟( 2 ⋅(

𝑎 = 𝑠2 = Beschleunigung 𝑠 = 𝑚 = Weg 𝑚

2

𝑟

𝑚+12⋅𝑚⋅𝑅

𝑠 =2⋅( 1

𝐻 = 𝐿 − 𝐿 ⋅ cos(𝛼𝑚𝑎𝑥 )

𝑚⋅𝑔

𝑚+12⋅𝑚⋅𝑅 2

) ⋅ 𝑡 2 + 𝑣0 ⋅ 𝑡 + 𝑠0

𝑚⋅𝑔

2

𝑚+12⋅𝑚⋅𝑅 2

𝑚⋅𝑔

2

𝑚+12⋅𝑚⋅𝑅 2 𝑚⋅𝑔

𝑟

2

𝑚+12⋅𝑚⋅𝑅

󰇍󰇍 = 𝑁𝑚 𝑀 = Drehmoment

𝑟2

𝑟

) ⋅ 𝑡 2 + 𝑣0 ⋅ 𝑡 + 𝑠0 )

) ⋅ 𝑡 + 𝜔0

) = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.

𝐹𝑧𝑢𝑔 = 𝐹 ⋅ cos(𝛼) 𝐹𝑁 = 𝐹 ⋅ sin(𝛼) 𝐹𝑔 = 𝐹𝑁 = 𝑚 ⋅ 𝑔 𝐹𝐻𝑅 = 𝜇𝐻𝑅 ⋅ (𝐹𝑔 − 𝐹𝑛 ) = 𝜇𝐻𝑅 ⋅ (𝑚 ⋅ 𝑔 − 𝐹 ⋅ sin(𝛼))

𝑝 = 𝑁𝑠 = Impuls 𝑚 𝑣 = 𝑠 = Geschwindigkeit 𝑚 = 𝐾𝑔 = Masse 𝜇𝐻𝑅 = Reibungswiederstand

Wellenlänge

( )

𝜆 = 𝑐𝑐 ⋅ 𝑇 𝜆=𝑓

𝜆 = 1𝑚 = Wellenlänge 𝑓 = = Frequenz in Hertz 𝑚 𝑠 𝑐 = = Ausbreitungsges. der Wellen 𝑠 𝑇 = 𝑠 = Periodendauer

Sender bewegt sich, auf ruhenden Beobachter zu 𝑓𝐵 = 𝑓𝑆 ⋅ 𝑐−𝑣𝑐

𝑆

Sender entfernt sich von ruhendem Beobachter 𝑐 𝑐+𝑣𝑆

1 = Frequenz Beobachter 𝑠 𝑓𝑆 = 1𝑠 = Frequenz Sender 𝑚 𝑣𝐵 = 𝑠 = Geschwindigkeit Beobachter 𝑚 𝑣𝑆 = 𝑠 = Geschwindigkeit Sender 𝑚 𝑐 = 𝑠 = Ausbreitungsges. der Wellen

𝐺𝑒𝑔𝑒𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛼 𝑎 = 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑐 𝐴𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛼 𝑏 = cos(𝛼) = 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑐 𝐺𝑒𝑔𝑒𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛼 𝑎 = tan(𝛼) = 𝐴𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛼 𝑏 𝜋 ⋅𝛼 Grad auf Bogen 𝑥 = 180°

𝐵 𝑓𝐵 = 𝑓𝑆 ⋅ 𝑐+𝑣 𝑐

Bewegter Beobachter entfernt sich von ruhendem Sender

sin2 (𝑥) + cos2 (𝑥) = 1

𝑓𝐵 = 𝑓𝑆 ⋅ 𝑐−𝑣𝐵

Tonleiter Eine Oktave geht von c1 bis c2 c2

523,251 Hz

h1

493,883 Hz

1

466,164 Hz 1

gis /as g

440,000 Hz 415,305 Hz

1

391,995 Hz

fis1/ges1

369,994 Hz

1

349,228 Hz

e1

329,628 Hz

dis1/es1

311,127 Hz

f

d1

293,665 Hz 1

1

𝐴 = 𝜋 ⋅ 𝑟2 =

Geometrische Körper

𝑐

a1 Kammerton

𝐺𝑒𝑔𝑒𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛽 𝑏 = 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑐 𝐴𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛽 𝑎 = cos(𝛽) = 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑐 𝐺𝑒𝑔𝑒𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛽 𝑏 = tan(𝛽) = 𝐴𝑛𝑘𝑎𝑡ℎ𝑒𝑡𝑒 𝑣𝑜𝑛 𝛽 𝑎 Bogen auf Grad 𝛼 = 180° ⋅𝑥 𝜋

sin(𝛼) =

Bewegter Beobachter kommt auf ruhenden Sender zu

ais1/b1

Trigonometrie

𝑓𝐵 =

Doppler Effekt

𝑓𝐵 = 𝑓𝑆 ⋅

( )

cis /des

277,183 Hz

c1

261,626 Hz

Schiefe Ebene

Rollreibungskraft 𝐹𝑅 = 𝜇 𝑅𝑅 ⋅ 𝐹𝑁 = 𝜇𝑅𝑅 ⋅ 𝑚 ⋅ 𝑔 ⋅ cos(𝛼) Gleitreibungskraft 𝐹𝐺 = 𝜇 𝐺𝑅 ⋅ 𝐹𝑁 = 𝜇𝐺𝑅 ⋅ 𝑚 ⋅ 𝑔 ⋅ cos(𝛼) Haftreibungskraft 𝐹𝐻 ≦ 𝜇 𝐻𝑅 ⋅ 𝐹𝑁 = 𝜇𝐻𝑅 ⋅ 𝑚 ⋅ 𝑔 ⋅ cos(𝛼) Normalkraft 𝐹𝑁 = 𝐹𝐺 ⋅ cos(𝛼) = m ⋅ g ⋅ cos(α) 𝜇𝐻𝑅 = tan(𝛼) = 𝐻𝐿 𝛼 = arctan(𝜇𝐻𝑅 )

440𝐻𝑧 ⋅ ( √2 )

3

12

440𝐻𝑧 ⋅ ( √2 )

2

12

440𝐻𝑧 ⋅ ( √2 )

1

12

440𝐻𝑧 ⋅ ( √2 ) 12

440𝐻𝑧 ⋅ ( √2) 12

0

−1

440𝐻𝑧 ⋅ ( √2) 12

−2

440𝐻𝑧 ⋅ ( √2) 12

−3

440𝐻𝑧 ⋅ ( √2) 12

−4

440𝐻𝑧 ⋅ ( √2) 12

−5

440𝐻𝑧 ⋅ ( √2) 12

−6

440𝐻𝑧 ⋅ ( √2) 12

−7

440𝐻𝑧 ⋅ ( √2) 12

−8

440𝐻𝑧 ⋅ ( √2) 12

−9

𝑚 = Kg=Masse 𝑚 𝑔 = 𝑠2 = Fallbeschleunigung 𝑚 = 9,807𝑠2 µ = Reibungswiederstand

Kreisfläche: Kugel Volumen

4 𝑉 = 3 ⋅ 𝜋 ⋅ 𝑟3 =

Radius Zylinder Volumen Mantel

abc Formel

𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0

pq Formel

𝑥 2 + 𝑝𝑥 + 𝑞 = 0

𝑟= ⋅ 1 2

𝑂 √𝜋

𝜋 4

𝜋 6

sin(𝛽) =

sin(𝑥) = cot(𝑥) tan(𝑥) = cos (𝑥)

⋅ 𝑑2

⋅ 𝑑3 =

=√

3 3⋅𝑉 4⋅𝜋

1

Kreisumfang: 1 6

⋅√𝜋

𝑂3

Durchmesser

𝑉 = 𝜋 · 𝑟2 ⋅ ℎ 𝑀= 2 · 𝜋 · 𝑟 · ℎ 𝑥=

Oberfläche

Oberfläche Grundfläche

−𝑏±√𝑏 2 −4𝑎𝑐 2𝑎

𝑥 = − 2 ± √( 2)2 − 𝑝

𝑝

(𝑥) = cot(𝑥) = cos sin(𝑥)

1 tan(𝑥)

𝑈= 2⋅𝜋⋅𝑟 = 𝜋⋅𝑑

𝑂 = 4 ⋅ 𝜋 ⋅ 𝑟2 = 𝜋 ⋅ 𝑑 2 3 = √36 ⋅ 𝜋 ⋅ 𝑉 2 𝑑 = √ 𝜋 = 2 ⋅ √3⋅𝑉 4⋅𝜋 𝑂

3

𝐴 = 2 · 𝜋 · 𝑟 · (𝑟 + ℎ) 𝐺 = 𝜋 · 𝑟2...