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Formula Sheet
Cascarano
Scalar Product
Math Stuff
βƒ—βƒ— = |𝐴⃗||𝐡
βƒ—βƒ—| cos πœƒ
𝐴⃗ βˆ™ 𝐡
Vector Product
βƒ—βƒ— = |𝐴⃗||𝐡
βƒ—βƒ—| sin πœƒ
𝐴⃗ × π΅
Quadratic formula
(ax2+bx+c=0)
π‘₯=
Kinematics
𝑣π‘₯ = π‘£π‘œπ‘₯ + π‘Žπ‘₯ 𝑑
1
π‘₯ = π‘₯π‘œ + π‘£π‘œπ‘₯ 𝑑 + 2π‘Žπ‘₯ 𝑑 2
2
𝑣π‘₯2 = π‘£π‘œπ‘₯
+ 2π‘Žπ‘₯ (π‘₯ βˆ’ π‘₯π‘œ )
π‘£π‘œπ‘₯ + 𝑣π‘₯
π‘₯ βˆ’ π‘₯π‘œ = (
)𝑑
2
Velocity Addition
𝑣⃗𝐴𝐡 = 𝑣⃗𝐴𝐢 + 𝑣⃗𝐢𝐡
βˆ’π‘ ± βˆšπ‘ 2 βˆ’ 4π‘Žπ‘
2π‘Ž
Acceleration of gravity
Constants
g = 9.80 m/s2
G = 6.67x10-11 Nm2/kg2
Universal gravitation
𝑀𝐸 = 5.97π‘₯1024 π‘˜π‘”
𝑅𝐸 = 6.38π‘₯106 π‘š
Mass of Earth
Radius of Earth
Trig Identities
Law of cosines:
Newton’s Laws / Friction / Circular motion
βˆ†π‘βƒ—
2 Law
βˆ‘ 𝐹⃗ = π‘šπ‘Žβƒ— =
π‘Ž2 = 𝑏 2 + 𝑐 2 βˆ’ 2𝑏𝑐 cos 𝛼
Gravitation
Law of sines:
Static friction
Kinetic friction
nd
βˆ†π‘‘
π‘Ž
𝑏
𝑐
=
=
sin 𝛼 sin 𝛽 sin 𝛾

a

b

πΊπ‘š1 π‘š2
𝐹=
π‘Ÿ2
𝑓𝑠 ≀ πœ‡π‘  𝑁
π‘“π‘˜ = πœ‡π‘˜ 𝑁
Centripetal acceleration
π‘Žπ‘π‘ =
1
Work done by a spring
π‘Šπ‘ π‘ = 2π‘˜π‘₯ 2
Conservative forces
π‘Šπ‘ = βˆ’βˆ†π‘ˆ
Non-conservative forces
Power
π‘Šπ‘›π‘ = βˆ†πΈ
π‘Šπ‘œπ‘Ÿπ‘˜
𝑃=
π‘‘π‘–π‘šπ‘’
Impulse and Momentum
𝑝⃗ = π‘šπ‘£βƒ—
Energy
1
𝐾 = 2π‘šπ‘£ 2
Kinetic energy
Gravitational potential
energy
Spring potential energy
Impulse momentum
π‘ˆπ‘” = π‘šπ‘”π‘¦ = βˆ’
πΊπ‘šπ‘€πΈ
π‘Ÿ
1
π‘ˆπ‘ π‘ = 2π‘˜π‘₯ 2
𝐹 = π‘˜π‘₯
π‘Šπ‘‘π‘œπ‘‘π‘Žπ‘™ = βˆ†πΎ
Hooke’s Law (spring force)
Work-Energy Theorem
Center of Mass
Center of mass
(point objects)
π‘₯𝐢𝑀 =
𝐼⃗ = πΉβƒ—π‘Žπ‘£π‘’ βˆ†π‘‘
𝐼⃗ = βˆ†π‘βƒ—
Impulse
𝑣2
π‘Ÿ
c
Work & Power
π‘Š = πΉπ‘‘π‘π‘œπ‘ πœƒ
Work by constant force
Linear
momentum
Physics 2A
βˆ‘π‘› π‘šπ‘› π‘₯𝑛
βˆ‘π‘› π‘š 𝑛
π‘βƒ—π‘‘π‘œπ‘‘π‘Žπ‘™ = π‘€π‘‘π‘œπ‘‘π‘Žπ‘™ 𝑣⃗𝐢𝑀
Total momentum
βˆ‘ 𝐹⃗𝑒π‘₯𝑑 = π‘€π‘‘π‘œπ‘‘π‘Žπ‘™ π‘Žβƒ—πΆπ‘€
Rotational Kinematics
πœ” = πœ”π‘œ + 𝛼𝑑
1
Linear / Angular
𝑠 = π‘Ÿπœƒ
(πœƒ 𝑖𝑛 π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘›π‘ )
πœƒ = πœƒπ‘œ + πœ”π‘œ 𝑑 + 2𝛼𝑑 2
𝑣𝑑 = π‘Ÿπœ”
πœ”2 = πœ”π‘œ2 + 2𝛼(πœƒ βˆ’ πœƒπ‘œ )
πœ”π‘œ + πœ”
πœƒ βˆ’ πœƒπ‘œ = (
)𝑑
2
π‘Žπ‘‘ = π‘Ÿπ›Ό
Torque
π‘Žπ‘π‘ =
𝑣2
= π‘Ÿπœ”2
π‘Ÿ
Torque and Angular Momentum
πœβƒ— = π‘Ÿβƒ— × πΉβƒ— = π‘ŸπΉπ‘ π‘–π‘›βˆ… = π‘ŸβŠ₯ 𝐹
Angular
momentum
𝐿⃗⃗ = π‘Ÿβƒ— × π‘βƒ— = π‘šπ‘£π‘ŸβŠ₯ = πΌπœ”
βƒ—βƒ—
Rotational Inertia and Energy
𝐼 = βˆ‘π‘– π‘šπ‘– π‘Ÿπ‘– 2
Rotational inertia
(point objects)
Parallel axis theorem
𝐼𝑃 = 𝐼𝐢𝑀 + 𝑀𝑑 2
1
𝐾 = 2πΌπœ”2
Rotational kinetic energy
Rotational Motion
Newton’s 2nd law
βˆ‘ πœβƒ— = 𝐼𝛼⃗ =
βƒ—βƒ—
𝑑𝐿
𝑑𝑑
Work
π‘Š = πœβˆ†πœƒ = βˆ†πΎπ‘Ÿπ‘œπ‘‘
Power
𝑃 = πœπœ”
Cascarano
Displacement
Formula Sheet
Simple Harmonic Motion
π‘₯(𝑑) = π΄π‘π‘œπ‘ (πœ”π‘‘ + βˆ…)
Velocity
Period
Angular Frequency
Mass on a spring
Simple pendulum
𝑣(𝑑) = βˆ’πœ”π΄π‘ π‘–π‘›(πœ”π‘‘ + βˆ…)
2πœ‹
𝑇=
πœ”
Frequency
(j) Thin hoop rotating on axis through any diameter of the hoop:
1
𝐼 = 𝑀𝑅 2
2
Physics 2A
π‘˜
πœ”=√
π‘š
𝑔
πœ”=√
𝑙
1
πœ”
𝑓= =
𝑇 2πœ‹
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