What's the Time for One Complete Revolution on a Hanging Swing Ride?

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In summary, the conversation discusses the process of determining the time it takes for one complete revolution around a pole based on given measurements and using Newton's laws and the relationship between angular velocity and radial acceleration. The participants also mention using a free body diagram and the Pythagorean theorem to solve for relevant forces. Finally, they mention using the formula for RPM to determine the rotational velocity in radians per second.
  • #1
robdawg
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hello all this is my first post. I need to know the time to do one complete revolution around the pole.

...m
I------------------
I...I...θ...\
I...I.....\
I...I......\..n
I.......[]
I
I

m = 3 meters
n = 5 meters
θ = 30
[] = swing
 
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  • #2
Draw a free body diagram, identify the centripetal force acting, Then apply Newtons laws to find the radial component of acceleration. Use the relationship between the angluar velocity and the radial component of acceleration to determine the angular velocity.
 
  • #3
here's what I know so far by doing a free body diagram.
5cos(30)= y
length y = Sqrt(18.75)
5sin(30) = x
length x = 2.5
R = 3 + 2.5 = 5.5

using the pythagorean thereom we now that

sqrt((2.5)^2 + 18.75) = 5

force y = tcos(30)
force x = tsin(30)

circumference = 2pi(R)

about the forces we know that 5cos(30) = mg
and that tsin(30) = mω^2R

now how do I get rpms from this? what do I solve for?

thanks
 
Last edited:
  • #4
ω is the rotational velocity in Radians/second. One revolution is 2Π Radians so to get RPM = 2Πω*60
 

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