HERE IS MY SITUATION.
A shaft supposed to rotate a circular disc of mass 30 kg.it will rest for every 3 sec in a position and rotate for 60 deg within a sec r so.this process will go on and on.
How to find the power and torque needed to rotate that shaft?
If I'm using a electrical drive like stepper motor and how to find the factor of safety?

I would start by familiarizing yourself with angular acceleration, torque, power, and the concept of moment of inertia. There's a pretty good wikiuniversity article explaining it all here:

http://en.wikiversity.org/wiki/Torqu...r_acceleration

You'll need to know the moment of inertia (usually designated as I) for a solid disk. You can find the answer at this link:

http://en.wikipedia.org/wiki/List_of_moments_of_inertia

You'll see that for a disk it's , where m is the mass and r is the radius.

Once you know the moment of inertia and the angular acceleration, you can calculate the required torque, as well as the power.

As for engineering safety factors, I think it's pretty normal to build in a safety factor of 2-3, so you'd want to size your motor at 2 to 3 times the required power and torque.

If after you read that first link you still have questions about how to calculate the angular acceleration, torque, or power, just ask and I'll be happy to help. It'll just be a lot easier after you're familiar with the terminology.