Astronaut An astronaut is rotated in a horizontalcentrifuge at a radius of 3.0 m

Question

Astronaut An astronaut is rotated in a horizontalcentrifuge at a radius of 3.0 m. (a) What is the astronaut's speed if thecentripetal acceleration has a magnitude of 5.0g?
1??? m/s
(b) How many revolutions per minute are required to produce thisacceleration?
2?? rev/min
(c) What is the period of the motion?
3??s (a) What is the astronaut's speed if thecentripetal acceleration has a magnitude of 5.0g?
1??? m/s
(b) How many revolutions per minute are required to produce thisacceleration?
2?? rev/min
(c) What is the period of the motion?
3??s

Explanation / Answer

   radius, r = 3 m     (a)   acceleration, a = 5 g = 5 ( 9.8 ) = 49m/s^2         But, a =V2 /r            V2 = a r = 49 * 3 =   147            V = 12.12 m/s (b) angular velocity, = V / r = 12.12 / 3=  4.04 rad / s = 4.04 * ( 60 / 2 ) rpm= 38.61 rpm (c)   Time period , T = 2 / = 2*3.14 / 4.04 = 1.55 s                                  

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