hanging swing fair ride

[robdawg]

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

[Integral]

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.

[robdawg]

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

[Integral]

ω is the rotational velocity in Radians/second. One revolution is 2Π Radians so to get RPM = 2Πω*60