# Formula Sheet – PHY 161 – Exam B Chapter 1: Introduction

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```Formula Sheet – PHY 161 – Exam B
Chapter 1: Introduction
4
Sphere (radius π): Area π΄ = 4ππ 2 , Volume π = π π 3 .
3
Cylinder (radius π, height β): Area π΄ = 2ππ 2 + 2ππβ, Volume π = ππ 2 β.
Density (mass π, volume π): π = π/π.
Chapter 2: One-Dimensional Kinematics
Definitions
Change (β) is final value minus initial value:
βπ₯ = π₯ − π₯0 , βπ‘ = π‘ − π‘0 , βπ£ = π£ − π£0 .
Instantaneous quantities: π£ =
ππ₯
ππ‘
Average quantities: π£Μ = π£ππ£π =
, π=
βπ₯
βπ‘
ππ£
ππ‘
=
, πππ£π =
π2 π₯
ππ‘ 2
βπ£
βπ‘
.
.
Speed (π  always positive or zero): π  = |π£| , π ππ£π =
Acceleration due to gravity: π = −π , π = 9.8
Kinematic equations of motion
If we let π = constant and π‘0 = 0, then
1
π₯ = π₯0 + π£0 π‘ + ππ‘ 2 , π£ = π£0 + ππ‘,
2
π£ 2 = π£02 + 2πβπ₯ , π£ππ£π =
π£0 +π£
2
.
π
π 2
π‘ππ‘ππ πππ π‘ππππ
π‘
.
, “g-factor”= π/π.
Chapter 3: Vectors
Components: ππ₯ = π cos π, ππ¦ = π sin π, π = √ππ₯2 + ππ¦2 , tan π = ππ¦ /ππ₯ .
ββ, if and only if πΆπ₯ = π΄π₯ + π΅π₯ and πΆπ¦ = π΄π¦ + π΅π¦ .
Addition: πΆβ = π΄β + π΅
ββ = π΄π₯ π΅π₯ + π΄π¦ π΅π¦ + π΄π§ π΅π§ = π΄π΅ cos π.
Scalar (dot) product: π΄β β π΅
Vector (cross) product:
ββ = (π΄π¦ π΅π§ − π΄π§ π΅π¦ )πΜ + (π΄π§ π΅π₯ − π΄π₯ π΅π§ )πΜ + (π΄π₯ π΅π¦ − π΄π¦ π΅π₯ )πΜ.
π΄β &times; π΅
Chapter 4: Two-Dimensional Kinematics
ββπ΄πΆ = π
ββπ΄π΅ + π
ββπ΅πΆ .
Relative motion: π
Uniform circular motion (speed π£, radius π, period π):
2
π = π£ ⁄π , π£ = 2ππ⁄π .
Chapter 5: Newton’s Laws, Part 1
Here πΉβ refers to the total force acting on an object, equal to the vector sum of
all individual forces acting on the object: πΉβ = ββββ
πΉ1 + βββββ
πΉ2 + βββββ
πΉ3 + β―
First Law: πΉβ = 0 if and only if πβ = 0, where πβ is the object's acceleration.
Second Law: πΉβ = ππβ, where π is the object's (inertial) mass, a constant.
Third Law: If two objects are interacting, then πΉβ21 = −πΉβ12 .
Weight: π€ = ππ, where π = 9.8π/π  2 .
```