Single Phase Motor Control 1hp 1745 rpm

Hello, How can I control a single phase motor and geared motor with arduino? Simple on/off will do, no need to control the speed or direction. Can I just use a relay ? or do I need a high power driver board?

Certainly a relay will work. BUT don't use one of the cheap, blue box relays usually used for Arduino learning projects. Use a relay that is rated for HP of your motor.
Paul

1 Hp is 745W so any 10A relay will work.

Actually, a relay rated for a 1hp motor is required. Just any 10A relay may not have enough clearance to suppress the Arc when the contacts are open.
Paul

an apology I am new to this, how can I make the code for only the on and off?

code
https://create.arduino.cc/projecthub/reverendfuzzy/simple-on-off-pushbutton-f637a7

circuit
OIP.NLi3kuIianRkOoqHRkvi9QHaDw