blog/content/Formulas.md

#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