# 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.........&theta;......\
I........I..................\
I........I....................\..n
I.............................[]
I
I

m = 3 meters
n = 5 meters
&theta; = 30
[] = swing

Related Introductory Physics Homework Help News on Phys.org

#### Integral

Staff Emeritus
Gold Member
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) = m&omega;^2R

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

thanks

Last edited:

#### Integral

Staff Emeritus
Gold Member
&omega; is the rotational velocity in Radians/second. One revolution is 2&Pi; Radians so to get RPM = 2&Pi;&omega;*60

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