In an amusement park ride, cars are suspended from L = 4.20 m cables attached to rotating arms at a distance of D = 6.13 m from the axis of rotation. The cables swing out at an angle of θ = 52° when the ride is operating. What is the angular speed of rotation?

Question

anonymous · Answer

You know that bodies in uniform circular motion accelerate inward, right?$$F _{c}=\frac{mv ^{2}}{r}$$
So, to find out the velocity and to find angular speed, we will find the tension component inward. That will be our centripetal force. Since we know the vertical part of tension (gravity), and the angle, the horizontal part is easily calculated. 

The radius is easy to compute as well, it is the sum of the length of the arm and the horizontal displacement of cable. 

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