I want to control speed of an AC Motor using phase cutting.. Well, I already have zero cross detector and SSR but don't know how to program Arduino to phase cutting using SSR.. And to connect the motor to SSR, do I need some protective circuit or not? Thanks!
As per Your question You must need a protective circuit to save the Arduino from Back Voltage.
Take reference from this Link AC Motor Speed Control
First of all no protective circuit is needed in order to connect an arduino with an SSR. SSR input is isolated from the load. Now answering your question you better go with an inverter, forget the SSR, and let arduino control the inverter. Using DOs from an arduino you can command the inverter to start/stop the motor or change the motor direction. Using an AO e.g provided by a DAC like MCP4921 you can control the motor RPM, too. There are a lot of inverters available for different loads and also different controls (Manual, Digital/Analog, Serial)