In order to solve this task you have to match theta as the angle from the top.
Then determine whether force is normal to the sphere, in this case it is normal so:
After that you need to appeal to this formula :
[tex]Fn = mgcos[/tex]
The formula for the force which is tangential to the sphere :[tex]Ft = mgsin[/tex]
The last step : the mass starts to slide,
[tex]Ft = µs * Fn
µs = Ft/Fn = tan
theta = arctan(µs)[/tex]
Hope it has become clear.
Regards.
