for PHYSICS GENIUSES!!!?

Question

At what rate must cylindrical spaceship rotate if if the occupants are to experience simulated gravity of .55g? Assume the spaceship's diameter is 30m and give your answer as the time needed for one revolution. please include details. THANK YOU!!!

Answer 1

I assume that the outside wall will act as the floor. And for the sake of this problem I'll use g=9.81 m/s^2.

Is this OK with you?
so the required acceleration is 5.40 m/s^2.

The centripetal acceleration is given by
a = v^2 / r
or
v = sqrt(a x r) = 7.3454 m/s

now t = 2 Pi r / v = 8.55 seconds

One revolution would last 8.55 seconds or the tube rocket will need to rotate at 7.01 RPM.

Answer 2

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Answer 3

Assume g = 9.8 m/s² ; knowing that a = v² / r, rotational speed should be

ω = v / r = √ (ar) / r = √(a/r) = √ ((.55 × 9.8)/15) = 0.6 rad/s

Solving for T in 2π = ωT, yields T = 10.472 s

P:.S.: I've just found efintosh49's answer. Having repeated his calculations, got a different answer. Acceleration is 5.4 m/s², indeed, but, how come √(5.4 × 15) = 7.3454...? I get 9 m/s in this computation. Then, 2πr/v = 2π × 15 / 9 = 10 π/3 = 10.472 s, as I got before.

Answer 4

I came up with a numerical value that is 11663 times smaller than the period of the rotation of Earth around its axis.

Use dimensional analysis to make a quantity with dimension of time from the quantities given in the problem. Then, use my hint to calculate the numerical constant, if you're a genius!