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Comparing Linear and Rotational Dynamics
Linear acceleration, a, (previously just called acceleration) is defined as the rate of change of (linear) velocity.  
This gives us the following equation  
 
Similarly, we define angular acceleration α as the rate of change of angular velocity.  
This can be expressed by the following equation  
 
Also, Newton's second law of motion is often stated as  
 
and a "rotational equivalent" to this equation was also found  
 
A comparison between these equations leads to the suggestion that we can find rotational (angular) quantities which are mathematically equivalent to the familiar linear quantities.  
   
In these equations, we see that  
α is equivalent to a
ω is equivalent to v
I is equivalent to m
 
   
We extend the list as follows:    
Linear Quantity  Angular Quantity 
θ
ω1 
ω2
α
τ 
I
L
 
   
We can now propose new equations by simply substituting rotational quantities for linear quantities.  
For example  
  gives  
  gives  
 
and so on...    
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