Linear & Rotational Dynamics

Summary of Equations

Here is a summary of the dynamics equations you need to know and understand.

The kinematics equations are here.

Concept Linear Rotational
Algebraic Calculus
Algebraic
Calculus
Change the state of motion
Force, F vector

Torque, tau

t = r cross F

torque = Fr sin theta

  
Inertia
Mass, m
 

Moment of Inertia, I

I = mr2
Newton's 2nd Law
Fnet = ma
Fnet = m dv/dt etc.
tau = I alpha
Kinetic Energy
K=(1/2)mv^2 etx
  
k=(1/2)I omega^2 etc
  
Work

F=dw/dx

W = int tau dtheta

tau=dW/dtheta
Work/Energy Equation
 
 
Potential Energy  
   
Conservation of Energy
Ko + Uo = K + U
  
Same
  
Power
Center of Mass
   
Momentum
p=mv etc
  

Angular Momentum, L

L=r cross p etc

 
Impulse
Impulse = F delta t
Impulse = int F dt

Impulse/Momentum Equation

(Newton's Second Law)

Fnet delta t etc
Fnet = dp/dt
tau net = delta L
tau net = dL/dt
Conservation of Momentum
psubo = p
  
 

last update April 4, 2007 by JL Stanbrough