A body moves on a circle of radius with speed and angular speed

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Scientific programming for physicists · Scientific programming for physicists

Computational Physics, Ch Letting the computer do the algebra

Problem

A body moves on a circle of radius

r

with speed

v

and angular speed

\omega

. Two expressions for its centripetal acceleration are written into SymPy as symbols with no numerical value:

a_1 = v^2/r

and

a_2 = \omega^2 r

, and the difference

\texttt{diff = a1 - a2}

is formed. Predict what

\texttt{print(diff)}

shows, without calling

\texttt{simplify}

, and say whether it is

0

. Then predict what happens if

v

is replaced everywhere by

\omega r

(its physical relation to

\omega

) and

\texttt{sp.simplify}

is then called on the result. Explain why the two predictions differ even though

a_1

and

a_2

describe the same acceleration physically.

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