Mechanics 2 help

[nid404]

A conical pendulum consists of  particle attached to the end of a light inextensible string of length 0.8 metres. The particle moves in a horizontal circle, and the system rotates at a constant angular speed of 4rad/s. Find the angle that the string makes with the vertical.

Thank you

[S.M.A.T]

Let the angle between the string and the vertical be 'Q' and the tension in the string be 'T'.
Since there is no vertical motion so weight of pendulum is equal to vertical component of 'T'.
sinQ=r/0.8
r=0.8sinQ

TcosQ=mg
T=(mg/cosQ)

The horizontal component of the tension is equal to centripetal force
TsinQ=m(w^2)r
(mg/cosQ)sinQ=m(4^2)×0.8sinQ
g/cosQ=12.8
cosQ=(g)/12.8
(If g=9.8 )
Q=40
 

[nid404]

Thanks  +rep