(UCM) Maximum Rev. Per Minute Using Length and Acceleration

AI Thread Summary
The discussion focuses on calculating the maximum revolutions per minute (RPM) of an astronaut rotating on a 10m arm without exceeding an acceleration of 5g. The acceleration is calculated using the formula Ac = v²/r, leading to a maximum velocity of approximately 7.07 m/s. The period of rotation is then determined using T = (2πR)/v, resulting in about 4.44 revolutions for 1g. Multiplying this by 5 gives an estimated maximum of 22.21 RPM. The conversation also includes a clarification question about the meaning of "g."
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Homework Statement



An astronaut rotates at the end of a test machine whose arm has a length of 10m. If the acceleration she experiences must not exceed 5g (g = 10 ms^-2), what is the maximum number of revolutions per minute of the arm?

Homework Equations



T = (2πR)/v

V = (2πR)/T

Ac = V2/r

The Attempt at a Solution



Ac = v2/r

Plug in acceleration given and radius (from length of 10m): 10 = v2/5

5*10 = 50

50 = v2

v = 7.07107

T = 2π*5/7.07107

T = 4.44288 revolutions for 1g

Multiply 4.44288 by 5 = 22.2144 RPM?
 
Last edited:
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Hi Oziemaster,

Do you know what "g" is?

ehild
 
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