Displacement
Δ𝑥=𝑥−𝑥0
𝑟=𝑟−𝑟0
Constant velocity
𝑣𝑥=Δ𝑥
Δ𝑡
𝑣𝑥= lim
Δ𝑡→0Δ𝑥
Δ𝑡=d𝑥
d𝑡
Acceleration
𝑎𝑥=𝛥𝑣𝑥
Δ𝑡
𝑎𝑥= lim
Δ𝑡→0Δ𝑣𝑥
Δ𝑡 =d𝑣𝑥
d𝑡
Relative velocity
𝑣𝑥𝑨𝑹=𝑣𝑥𝑨𝑩+𝑣𝑥𝑩𝑹
𝑣𝑥𝑨𝑩=−𝑣𝑥𝑩𝑨
Uniformly accelerated
movement
𝑣𝑥=𝑣𝑥0+𝑎𝑥𝑡
Δ𝑥=𝑣𝑥𝑜𝑡+1
2𝑎𝑥𝑡2
Δ𝑥=𝑣𝑥0+𝑣𝑥
2⋅𝑡
𝑣𝑥2=𝑣𝑥0
2+2𝑎Δ𝑥
Period and frequency
𝑇=2𝜋𝑟
𝑣
𝑓=1
𝑇
Centripetal
acceleration
𝑎𝐶=−𝑣2
𝑟𝑟
Laws of motion
∑𝐹𝑖=𝑚𝑎
𝒊
𝐹𝐴 sur B=−𝐹𝐵 sur A
Density
𝜌=𝑚
𝑉
Gravitational force
𝐹𝑔=−𝐺𝑚1𝑚2
𝑟2𝑟
𝐹𝑔=𝑚𝑔
𝑔=𝐺𝑚
𝑟2
Force of a spring
𝐹𝑠=𝑘|Δ𝑙| 𝑢
Δ𝑙=𝐿−𝐿𝑛𝑎𝑡
Friction
𝑓𝑐=𝜇𝑐|𝑁
|𝑢
0≤𝑓𝑠≤𝜇𝑠|𝑁
|𝑢
Archimedes’ equation
𝐹𝐴=−𝜌𝑓𝑉𝑔
Pressure
𝑃
=𝐹
𝐴𝑢
𝑃
𝐵=𝑃𝑆
+𝜌𝑔ℎ
Work
𝑊=𝐹⋅𝑟
𝑊=𝐹𝑥Δ𝑥+𝐹𝑦Δ𝑦+𝐹𝑧Δ𝑧
Kinetic energy
𝐾=1
2𝑚𝑣2
Energy of spring
𝑈𝑠=1
2𝑘Δ𝑙2
Energy potential of
gravity
𝑈𝑔=𝑚𝑔ℎ
𝑈𝑔=−𝐺𝑚1𝑚2
𝑟
Energy conservation
𝐸=𝐾+𝑈
𝐸𝑓=𝐸𝑖+𝑊𝑛𝑐
d𝐸
d𝑡=0
Exit speed
𝑣𝑒𝑥𝑖𝑡=√2𝐺𝑚
𝑟
Power
𝑃=𝑊
Δ𝑡
𝑃=𝐹⋅𝑣
Momentum
𝑝=𝑚𝑣
𝐹=Δ𝑝
Δ𝑡
Uniformly accelerated
rotation
𝜔=𝜔0+𝛼𝑡
Δ𝜃=𝜔0𝑡+1
2𝛼𝑡2
Δ𝜃=𝜔0+𝜔
2⋅𝑡
𝜔2=𝜔0
2+2𝛼Δ𝜃
Relation between
angular parameters
𝑥=𝑟𝜃
𝑣𝑥=𝑟𝜔
𝑎𝑥=𝑟𝛼
Centripetal
acceleration
𝑎𝑐=𝑟𝜔2
Torque
𝜏=𝑟×𝐹
Equilibrium
∑𝐹𝑖=0
𝒊
∑𝜏𝑖=0
𝒊
Center of mass
𝑟𝐶𝑀 =∑𝑚𝑖𝑟𝑖𝑖
∑𝑚𝑖𝑖
Kinetic energy of
rotation
𝐾=1
2𝐼𝜔2
𝐾=1
2𝐼𝐶𝑀𝜔2+1
2𝑚𝑣𝐶𝑀
2
Inertia
Particle: 𝐼𝐶𝑀=𝑚𝑟2
Cylinder: 𝐼𝐶𝑀=1
2𝑚𝑟2
Sphere: 𝐼𝐶𝑀=2
5𝑚𝑟2
Shell: 𝐼𝐶𝑀=2
3𝑚𝑟2
Rod: 𝐼𝐶𝑀=1
12𝑚𝑟2
Rod: 𝐼𝑒𝑥𝑡𝑟𝑒𝑚𝑖.=1
3𝑚𝑟2
Work and power of
rotation
𝑊=𝜏Δ𝜃
𝑃=𝜏𝜔
Dynamic of rotation
∑𝜏
𝑖=𝐼𝛼
Kinetic momentum
𝐿
=𝐼𝜔
𝐿
= 𝑟 × 𝑝
Numerical values
𝑔 =9.8 m/s2
𝐺=6.67⋅10−11N⋅m2
kg2
𝑃𝑎𝑡𝑚 =101.3 kPa
Quadratic equation
𝑎𝑥2+𝑏𝑥+𝑐=0
𝑥1,2=−𝑏±√𝑏2−4𝑎𝑐
2𝑎
Circle
𝐶=2𝜋𝑟
𝐴=𝜋𝑟2
Sphere
𝐴=4𝜋𝑟2
𝑉=4
3𝜋𝑟3
Trigonometry
𝑆𝑂𝐻−𝐶𝐴𝐻−𝑇𝑂𝐴
𝐻2=𝐴2+𝑂2
sin2𝜃+cos2𝜃=1
sin2𝜃=2sin𝜃cos𝜃
sin𝛼
𝐴=sin𝛽
𝐵=sin𝛾
𝐶
𝐶2=𝐴2+𝐵2−2𝐴𝐵cos𝛾
