# Tension in a rotating swing

I am doing a review for a Dynamics exam, but I am having trouble with this one question (below).

What I have done is make a free body diagram that includes the tension of the cable and the weight of the rider/swing. So according to my calculations for part i:

T= mg cos (30) = 680N

The tangential acceleration is 0

Which according to the provided solutions is incorrect. Am I missing a force?

I figured the tension is integral to finding the velocity of the rider. So I want to get my tension right before I proceed with finding the velocity, though I am also having trouble figuring out how to relate tension and velocity of the acceleration of the rider is 0

Please note the top picture (smaller) contains the answers.

I would appreciate an explanation. • Radial acceleration is not zero. – sammy gerbil May 3 '17 at 20:25

## 1 Answer

The starting equation is incorrect. The vertical component of T must support the weight of the rider and the horizontal component of T provides the centripetal force that keeps the rider going in a circle.