2 centripetal acceleration problems

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To achieve centripetal acceleration equal to Earth's gravitational acceleration, the rotating cylinder must have a specific angular speed calculated using the formula a = v²/r. For the air puck problem, the tension in the string, horizontal force on the puck, and the puck's speed can be determined using Newton's laws and centripetal force equations. Participants are encouraged to share their attempts and relevant formulas to facilitate problem-solving. The discussion emphasizes the importance of applying physics principles to both scenarios. Understanding these concepts is crucial for solving centripetal acceleration problems effectively.
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Any help would be greatly appreciated...:cry:

It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

An air puch of mass 0.25 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves. a) What is the tension in the string? b) What is the horizontal force acting on the puck? c) What is the speed of the puck?
 
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First, you need to show us what you've attempted so far on these problems. What formulas do you know?
 
um i think on the first one you use the a=v2/r equation
is that correct?
 

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