© Copyright 2024 M. M. Afshar. All rights reserved.
Physics 101
Final Exam Formula Sheet
Conversions:
§ 1 mile = 5280 feet = 1609.344 meters
§ 1 meter = 3.281 feet = 39.37 inches
§ 360 degrees = 2𝜋 radians
"
§ Fahrenheit to Celsius: 𝑇! = # (𝑇$ − 32)
§ Kelvin to Celsius: 𝑇! = 𝑇% − 273.15
§ 1 atmosphere = 101325 pascals
Physics:
§ Uniform mass density: 𝑀 = 𝜌𝑉
§ Non-uniform mass density: 𝑀 = ∫ 𝜌 𝑑𝑉
§ Velocity and acceleration:
56⃗
;6⃗
<⃗
59
§ Kinematic equations in 𝑥:
?
𝑥= = 𝑥> + 𝑣2> 𝑡 + &𝑎2 𝑡 &
?
Constants:
§ Grav. acceleration on Earth: 𝑔 = 9.8 𝑚/𝑠 &
§ Earth’s mass: 𝑀' = 5.974 × 10&( 𝑘𝑔
§ Earth’s radius: 𝑅' = 6.378 × 10) 𝑚
§ Density of liquid water: 𝜌 = 1000 𝑘𝑔/𝑚*
Mathematics:
§ Circle – Circumference: 𝐶 = 2𝜋𝑅
§ Circle – Area: 𝐴 = 𝜋𝑅&
§ Sphere – Surface Area: 𝑆 = 4𝜋𝑅&
(
§ Sphere – Volume: 𝑉 = * 𝜋𝑅
*
§ Cylinder – Surface Area: 𝑆 = 2𝜋𝑅& + 2𝜋𝑅𝐿
§ Cylinder – Volume: 𝑉 = 𝜋𝑅& 𝐿
§ sin 𝜃 = 𝑂/𝐻 , cos 𝜃 = 𝐴/𝐻 , tan 𝜃 = 𝑂/𝐴
+
§ sin L& ± 𝜃N = cos(𝜃)
+
§ cos L & ± 𝜃N = ∓ sin(𝜃)
§ sin& 𝜃 + cos & 𝜃 = 1
§ Quadratic formula: 𝑥 =
,-±√- ! ,(01
&0
T⃗ = 𝐴𝐵 cos 𝜃 = 𝐴2 𝐵2 + 𝐴3 𝐵3
§ 𝐴⃗ ⋅ 𝐵
T⃗ = U𝐴3 𝐵4 − 𝐴4 𝐵3 V𝚤̂ + (𝐴4 𝐵2 − 𝐴2 𝐵4 )𝚥̂
§ 𝐴⃗ × 𝐵
+U𝐴2 𝐵3 − 𝐴3 𝐵2 V𝑘Z
<⃗
;9
𝑣⃗ = 58 , 𝑣⃗09: = ;8 , 𝑎⃗ = 58 , 𝑎⃗09: = ;8
𝑥= = 𝑥> + &U𝑣2> + 𝑣2= V𝑡
𝑣2= = 𝑣2> + 𝑎2 𝑡
&
&
𝑣2=
= 𝑣2>
+ 2𝑎2 U𝑥= − 𝑥> V
§ 𝑎605 = −𝑣 & /𝑅
§ 𝑤 = 𝑚𝑔
§ 𝑓@ ≤ 𝜇@ 𝑛
§ 𝑓A = 𝜇A 𝑛
§ 𝑅9>@ = 𝑏𝑣
?
§ 𝑅560: = 𝛼𝑣 & where 𝛼 = & 𝐷𝐴𝜌
§ 𝐹⃗@ = −𝑘𝑥 𝚤̂
§ ∑ 𝐹⃗ = 𝑚𝑎⃗
§ 𝐹⃗?BC& = −𝐹⃗&BC?
6⃗
§ 𝑊 = ∫6⃗ ! 𝐹⃗ ⋅ 𝑑𝑠⃗
"
§ 𝑊 = 𝐹 𝑑 cos 𝜃
§ 𝑊CD8 = Δ𝐾
§ 𝑊1 = −Δ𝑈
§ 𝑈: = 𝑚𝑔𝑦
?
§ 𝑈@ = & 𝑘𝑥 &
?
§ 𝐾 = & 𝑚𝑣 &
§ Δ𝐾 + Δ𝑈 = 𝑊C1
EF
EF
§ 𝐹2 = − E2 , 𝐹3 = − E3
§ 𝑃 = 𝑑𝐸/𝑑𝑡 , 𝑃09: = 𝑊/Δ𝑡
© Copyright 2024 M. M. Afshar. All rights reserved.
Moments of Inertia of Homogeneous Rigid Objects
§ 𝑝⃗ = 𝑚𝑣⃗
5G⃗
§ ∑𝐹⃗D28 =
58
§ 𝐼⃗ ≡ ∫ ∑𝐹⃗D28 𝑑𝑡
§ Elastic collision: 𝐾> = 𝐾=
§ Perf. inelastic collision: 𝑣⃗?= = 𝑣⃗&=
§ Elastic, head-on collision:
H ,H
&H
!
𝑣?= = H" IH! 𝑣?> + H IH
𝑣&>
"
&H"
!
"
!
H! ,H"
𝑣&= = H IH 𝑣?> + H IH 𝑣&>
?
"
!
§ 𝑟⃗1H ≡ J ∑> 𝑚> 𝑟⃗>
?
"
!
?
§ 𝑟⃗1H = J ∫ 𝑟⃗ 𝑑𝑚 = J ∫ 𝑟⃗ 𝜌 𝑑𝑉
&
§ 𝐼 = ∑> 𝑚> 𝑟>K
§ 𝐼 = ∫ 𝑟K& 𝑑𝑚 = ∫ 𝑟K& 𝜌 𝑑𝑉
§ 𝐼 = 𝐼1H + 𝑀𝐷&
5L
;L
§ 𝜔 = 58 , 𝜔09: = ;8
5!L
5M
;M
§ 𝛼 = 58 = 58 ! , 𝛼09: = ;8
§ Angular kinematic equations:
?
𝜃= = 𝜃> + 𝜔> 𝑡 + &𝛼𝑡 &
?
𝜃= = 𝜃> + &U𝜔> + 𝜔= V𝑡
𝜔= = 𝜔> + 𝛼𝑡
𝜔= & = 𝜔> & + 2𝛼U𝜃= − 𝜃> V
§ 𝑠 = 𝑟𝜃
§ 𝑣 = 𝑟𝜔
§ |𝑎80C | = 𝑟𝛼
§ |𝑎605 | = 𝑟𝜔&
?
?
&
§ 𝐾 = 𝐾N>C + 𝐾0C: = & 𝑀𝑣1H
+ & 𝐼1H 𝜔&
§ 𝐿T⃗ = 𝑟⃗ × 𝑝⃗
§ 𝐿T⃗ = 𝐼𝜔
T⃗
<⃗
5O
§ ∑𝜏⃗D28 = 58
§ 𝜏⃗ = 𝑟⃗ × 𝐹⃗ ⟹ 𝜏 = 𝑟𝐹 sin 𝜃 = 𝑟K 𝐹
§ ∑𝜏D28 = 𝐼𝛼