Solve Rotational Motion: Angular Velocity & Revolution Time

AI Thread Summary
To determine the time for one complete revolution of a merry-go-round with a radius of 5 meters and an angular velocity of 1/4 π radians per second, the total angle for one revolution (2π radians) is divided by the angular velocity. This results in a time of 8 seconds for one full revolution. Consequently, the number of revolutions per minute can be calculated as 60 seconds divided by the time for one revolution, yielding 7.5 turns per minute. The calculations clarify the relationship between angular velocity, revolution time, and the merry-go-round's motion. Understanding these concepts is essential for solving rotational motion problems effectively.
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Homework Statement


A merry-go-round has a radius of 5 meters and an angular velocity of 1/4 pii radians per second. How long does it take the merry go round to make one revolution? How many turns per min?


Homework Equations


radius of 5 meters and an angular velocity of 1/4 pii radians per second


3. The attempt at a s
1/4 * 57.295 = 14.323
I am really lost with this problem.
 
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If it takes 1 second to go 1/4 pi radians, how long does it take to go 2pi radians (the complete circle)?
theta = omega*t
and theta = 2pi here

If it takes t seconds for one revolution, the number of revolutions/min is 60/t
 
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