 #1
MathematicalPhysicist
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I have this exercise which I don't understand its solution.
I am attaching both the exercise and its solution.
It's problem 2: rocket trip.
What I don't understand in the solution they write that:
"and from this you get:
$$\omega < \frac{1}{R}\sqrt{12m/R}$$
Then plug in ##\omega = m/R^3## to obtain the possible radii for free falling motion,
$$R>3m$$
Now, if I plug in this ##\omega## I get: ##m/R^2<\sqrt{12m/R}## and squaring both sides and multiplying by R^4 I get: ##m^2<R^42mR^3## ; if ##R>3m## then ##R^42mR^3>27m^4## and this is greater than ##m^2## whenever ##m^2>1/27##; from what does this follow I don't see, can't ##m^2## be less than ##1/27##?
I am attaching both the exercise and its solution.
It's problem 2: rocket trip.
What I don't understand in the solution they write that:
"and from this you get:
$$\omega < \frac{1}{R}\sqrt{12m/R}$$
Then plug in ##\omega = m/R^3## to obtain the possible radii for free falling motion,
$$R>3m$$
Now, if I plug in this ##\omega## I get: ##m/R^2<\sqrt{12m/R}## and squaring both sides and multiplying by R^4 I get: ##m^2<R^42mR^3## ; if ##R>3m## then ##R^42mR^3>27m^4## and this is greater than ##m^2## whenever ##m^2>1/27##; from what does this follow I don't see, can't ##m^2## be less than ##1/27##?
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