An astronaut is rotated in a horizontal cnetrifuge ata radius of 5.0m. (a) what

Question

An astronaut is rotated in a horizontal cnetrifuge ata radius of 5.0m. (a) what is the astrounat's speed ifthe centripetal acceleration has a magnitude of 7.0g? (b) Howmany revolutions per minute are required to produce thisacceleration? (c) What is the period of the motion? I understand the question for part (a) and the answer is 18.5m/s. However parts (b) and (c) aren't too clear. Any help would be greatly appreciated! An astronaut is rotated in a horizontal cnetrifuge ata radius of 5.0m. (a) what is the astrounat's speed ifthe centripetal acceleration has a magnitude of 7.0g? (b) Howmany revolutions per minute are required to produce thisacceleration? (c) What is the period of the motion? I understand the question for part (a) and the answer is 18.5m/s. However parts (b) and (c) aren't too clear. Any help would be greatly appreciated!

Explanation / Answer

radius r = 5 m (a). Accleration a = 7g                r w ^ 2 = 7 *9.8 m/ s ^ 2                             =67.9 m / s ^ 2 from this angular speed w = [ 67.9 / r ]                                        = 3.685 rad / s                                        = 3.685 * ( 1/ 2 ) rev / ( 1/ 60 ) min                                         =35.19 rev / min (c). period of motion T = 2 / w                                     = 2 / 3.685 rad ./ s                                     = 1.705 s

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