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Mechanics

Comparing Linear and Rotational Dynamics

Linear acceleration, a, is given by

Angular acceleration, a, is given by

A comparison between these two equations leads to the suggestion that we can find rotational (angular) quantities which are mathematically equivalent to the more familiar linear quantities. In these two equations, we have

a  is equivalent to a
w1  is equivalent to u
w2  is equivalent to v

and time, of course, is the same in both cases.

We can extend the list as follows:

Linear quantity

Angular (rotational) quantity

s

 q

u

 w1

v

 w2

a

 a

F

 T (Torque)

m

 I (Moment of Inertia)

p

 L (Angular momentum)

We can now propose new equations by simply substituting rotational quantities for linear quantities. For example

s = ut + ½at² gives us q = w1t + ½at²
p = mv gives us L = Iw

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© David Hoult 2008