Important Equations

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Newton's First Law:
SF_net = ma

Bank Shots:
Angle of Incidence = Angle of Reflection

Conversion from rectangular coordinates to spherical coordinates:
x = rsinfcosq
y = rsinfsinq
z = rcosf

Center of Mass:


Kinetic Energy:


Conservation of Energy:
E_i = E_f

Coefficient of Restitution:
e = -(v_1f - v_2f)/(v_1i - v_2i)

Impulse:


Linear Momentum:
p = mv = dF/dt

Conservation of Momentum:


Moment of Inertia:


Torque:
t = r x F = rFsin q
t = Ia

Friction:
f_s = m_sN Stationary Friction
f_k = m_kN Kinetic Friction

Mechanical Energy Dissipation:
E_therm = f_kDx

Angular Momentum:
L = r x p = r x mv
L = Iw

Conservation of Angular Momentum:
L_i = L_f

Rotational Energy:
K_rot = (1/2)Iw²

Tangential Velocity/Acceleration:
v_cm = Rw
a_cm = Ra