F = m dv/dt 

F= ma 

 (Newtons or kg m/s² )

W = mg   

 (Newtons)

KE = ½ mv² 

⁽Joules)

U = ½ kx²  

 (Joules )

Remember k is in N/m

w = ∫ f dx 

  (joules or N-m)

Remember F parallel to X

w = F x cos (theta)

P = ∆ E/t   or ∆ME/t or ∆KE/t or  W/t or F v

P = dW/dt

(Watts or J/s)

μ = F_f  / F_n 

 (Dimensionless)

F∆t = m ∆v 

∆ρ= ∫F dt

  (N-s or kg-m/s)

Remember area under F vs t graph

1.    F = G m₁ m₂/ r² 

G = 6.67x 10^-11 N m²/kg²

^{r measured from center of mass}

1.    g = G m_e / r² 

(m/s)

G = 6.67x 10^-11 N m²/kg²

General term for

Gravitational potential energy

PE = -G m₁ m₂/ r

(J)

Don't forget the negative

and

PE = 0 at infinity

A_c = ω² r 

 A_c = v²/r 

 (m/s² )

Pointed toward the center

T = F X sin (theta) 

(N-m) not Joules

F perpendicular to X

Period of a pendulum

T = 2 π √(L/g) 

 (s)

T = 2 π √(m/k) 

(s)

Period of a physical pendulum

T = 2 π √(I/mgd)

(s)

Center of mass

X_cm = ∑(x m) / ∑(m) 

or

X_cm = ∫ r dm

Moment of Inertia 

I = mr²  (point mass) 

I = ∫ r² dm (distributed mass)

(kg m² )

  Rotational momentum

L = I ω

( kg m² /s)

Newton’s law for angular motion

T = I α

(kg m² /s² )

KE_r = ½ I ω²

^(J)

 Motion as it relates to drag

F = m dv/dt

mg- bv² = m dv/dt

if mg- bv = ma

then

v_t = mg/b

Spring constant

(hooke's law)

K = f/x

(N/m)

slope of the f vs x graph

T² = (4 π²/GM_s) r³

Period in seconds

  x = v_it + ½ at² 

 V_f ² = V_i²  + 2 a x

s = r Θ

v = r ω

a = r α

  I_pa = I_cm + mr²

Where r is the distance from the cm to the axis of rotation