#public
# Work and energy
| Formula                                | equation                                        | Usage                               |
| -------------------------------------- | ----------------------------------------------- | ----------------------------------- |
| Gravitational Potential Energy ($U_g$) | $U_g=mgh$                                       | Changes in height                   |
| Kinetic Energy                         | $K=\frac{1}{2}mv^2$                             | Energy of motion                    |
| Work-Energy Theorem                    | $\Delta E_{mec} = \Delta K+\Delta U=W_{other}*$ | calculating the effects of friction |


| Variable | Symbol | SI Unit | Notes |
| --- | --- | --- | --- |
| Mass | m | kg | Convert from grams (g) if necessary. |
| Height / Distance | h,d | m | Measures vertical or horizontal displacement. |
| Velocity / Speed | v | m/s | Convert from km/h by dividing by 3.6.+3 |
| Gravity | g | m/s2 | Earth's standard is approximately 9.8 m/s2. |
| Energy / Work | $U_g$,K,W | J | 1 Joule = 1 kg⋅m2/s2. |

# Center Of Mass (CM)
| Formula                                | equation                                        | Usage                               |
| -------------------------------------- | ----------------------------------------------- | ----------------------------------- |
| Position of COM X| $x_{com}=\frac{1}{M}\sum_{i=1}^{n}M_ix_i$  | find COM X|
| Position of COM Y| $y_{com}=\frac{1}{M}\sum_{i=1}^{n}M_iy_i$  | find COM Y| 
| velocity of COM  | $v_{com}=\frac{\sum m_iv_i}{M}$            | find the Velocity of COM |

| Variable | Symbol | SI Unit | Notes |
| --- | --- | --- | --- |
| Position (X or Y) | $x_{com},y_{com}$ | m | Coordinates on the Cartesian plane.+ 1|
| Total Mass | M | kg | The sum of all individual masses (m1​+m2​+…) |
| Velocity of CM | vcom​ | m/s | The speed at which the entire system's balance point moves |
# Linear Momentum and impulse
| Formula                                | equation                                        | Usage                               |
| -------------------------------------- | ----------------------------------------------- | ----------------------------------- |
| Linear Momentum | p = mv | find linear momentum |
| Impulse | $J=\Delta p=F_{avg}\Delta t=\int F(t)dt$ | change in momentum. Also area under Force-time graph |
| Conservation Law | $P_{initial}=P_{final}$ | if net external force is 0, totoal momentum is constant |
| Elastic Collisions (1D) | $v_{1f}=(\frac{m_1-m_2}{m_1+m_2})v_i+(\frac{2m_2}{m_1+m_2})v_2i$| momentum and kinetic energy are conserved |
| completely inelastic collisions | $m_1v_{1i}+m_2v_{2i}=(m_1+m_2)v_f$ | find situation where the objects stick together |


| Variable | Symbol | SI Unit | Notes |
| --- | --- | --- | --- |
| Momentum | p | kg⋅m/s | Calculated as mass × velocity. |
| Impulse | J | N⋅s | Also equivalent to kg⋅m/ s.|
| Force | F | N | 1 Newton = 1 kg⋅m/s2.+2 |
| Time | t,$\Delta$t | s | The duration of the force application.+1|