Newton's Three Laws 

Law of Inertia
Law of Acceleration
Law of ActionReaction 
centripetal force 

F_{c} = ma_{c} 
centripetal acceleration 

a_{c} = v ² / r 
tangential velocity 

v = 2pr / T
v = rw where w = 2pf ( frequency in hz) 
centripetal acceleration 

a_{c} = 4p ² r / T ² 
relationship between
period (T) and frequency (f) 

f = 1 / T 
centripetal acceleration 

a_{c} = 4p ² r f ² 
friction 

f = m N 
conical pendulums 

T cos q = mg
T sin q = F_{c} = m v ² / r 
source of centripetal force
for a banked curve
when traveling at critical speed 

F_{c} = N sin q
[remember that N cos q = mg] 
critical speed for a banked curve 

tan q = v ² / rg 
universal gravitation 

F = G M_{ 1} M _{2} / r
² 
universal gravitation constant 

6.67 x 10^{11}
N m ² / kg ² 
Kepler's Third Law 

T ² / R ³ = 4p ² / G M_{central
body}
a unique constant for every satellite
system 
gravitational field strength 

g = G M_{central body} / r ²
where r = R_{central body} + h 
Kepler's Second Law 

v_{A}R_{A} = v_{P}R_{P}
a satellite's tangential velocity and orbital radius
are inversely proportional 



critical velocity at the top of a
vertical circle
to achieve apparent weightlessness 

v = SQRT (rg) 
apparent weight at the bottom of a
vertical circle 

N = mg + m v ² / r 
Conservation of Energy 

S(PE
+ KE)_{before} = S(PE
+ KE)_{after}
PE = mgh
KE = ½ mv ² 
height of a pendulum 

h = L  L cos q 
kinematics equations 

s = v_{o }t + ½ a t ²
v_{f }² = v_{o}² + 2as
v_{f} = v_{o} + at
s = ½ ( v_{o} + v_{f} ) t 
range of a projectile 

R = v_{H} t 
period of a pendulum 

T = 2p(
L / g ) 
tension in pendulum at angle a 

take components of weight
T  mg cos a = m v ² / r
mg sin a = ma_{tangential} 