Question

An amusement park ride consists of a rotating
circular platform 8.09 m in diameter from
which 10 kg seats are suspended at the end
of 2.19 m mass less chains. When the system
rotates, the chains make an angle of 14.8
◦ with
the vertical.
The acceleration of gravity is 9.8 m/s
2
.

Answer 1

what are you asking for?

Answer 2

did I miss the question?

Answer 3

r = 2.19 sin 14.8 = .559 meters radius

centripetal a = Ac = omega^2 r =v^2/r

Look at tension in wire now
tan 14.8 = mg/mAc = 9.8/Ac
so
Ac = 9.8/tan 14.8 = 37.1 m/s^2

so v^2/r = 37.1
v^2 = 37.1* .559 = 20.7
v = 4.55 m/s

or for angular rate omega
omega^2 r = 37.1
omega^2 = 66.4
omega = 8.14 radians/ second