Crystal-controlled oscillators are, in general, far superior in frequency accuracy and stability than almost anything except an atomic clock or an oscillator "disciplined" by reception of a GPS timing signal (which is derived from an atomic "clock," usually rubidium in the satellite).
GPS receivers are cheap and are fairly easy to interface to make such disciplined oscillators. Hams, and others needing precision timing, will sometimes use a
GPS disciplined oscillator for the greatest practical timing and/or frequency accuracy. However, I mention this only for information purposes; it is decidedly overkill for timing swimming contests or training.
The power line frequency, whether it be 50 Hz in Australia or 60 Hz in the United States, has exceptional long-term accuracy. The number of AC cycles is counted continuously each day by the utility providing power to the electrical grid. At a certain time each day, the alternating frequency at the generating plant is either slightly increased or slightly decreased to make the number of complete AC cycles exactly equal to (60 cycles per second) x (60 seconds per minute) x (60 minutes per hour) x (24 hours per day) = 5,184,000 cycles per day, or for 50 Hz = 4,320,000 cycles per day. Therefore, a clock mechanism driven by a synchronous motor (such as yours alleges to be) will NEVER gain or lose time unless it is disconnected from the mains or there is an electrical grid failure.
Your choice of a synchronous motor for your sweep second hand is correct. Too bad the Chinese rip-off doesn't work properly. Perhaps you can try a different vendor?
You have two choices now on how to proceed. First, I recommend that you pitch the Chinese motor and purchase one that actually works correctly. The other choice is to build your giant display clock with an inexpensive stepper motor.
If you can actually find a synchronous 50 Hz clock motor with a 1 RPM shaft speed that operates on 240 VAC, buy it! That will be the simplest solution.
This type of synchronous clock motor is actually a spur-gear speed reduction motor, so the holding torque is relatively high. That does NOT mean a gust of wind blowing against a one meter long "second" hand will not slow down the motor shaft. It may even turn the motor shaft backwards! Compound spur-gears make great speed reducers, but only a worm-gear prevents backward torque by design. You will generally find worm gears on DC brushed motors, but of course a gear box (of any kind) can be added to a motor shaft.
If you want to use a stepper motor, you will need a PWM motor driver, a DC power supply of 20 to 30 volts capable of one or two amperes, a stepper motor controller, and some means to divide the 50 Hz mains frequency to a slower train of pulses such that it takes one minute to rotate the motor shaft one revolution.
Often the motor controller already has the capability of driving small stepper motors, like the one you would use, without a separate MOSFET h-bridge driver. One advantage of using the PWM motor driver is the motor coils are always energized, even between steps. This greatly increases the holding torque of the motor in between steps, compared to drivers that de-energize the motor coils between steps, and rely on the permanent magnets in the stepper motor rotor to provide holding torque between the rotor and the stator. Although this does work for light loads, anything subject to large external forces, such as winds gusts, needs shaft-holding torque available all the time.
Can you get 'smooth' stepper motors?
No. The motor rotor moves in discrete steps. You can purchase motor controllers that perform so-called micro-stepping that will give the appearance of smoothness, but this usually results in a loss of torque. The way this works is you provide the motor coils with pseudo-sinusoidal quadrature wave forms, typically by using PWM to create quadrature sinusoidal currents. This allows the rotor to be driven into positions in between its internal magnetic poles, hence the term "micro-stepping" as applied to this mode of operation. It is fairly easy to get "lost" while micro-stepping a stepper motor, so I don't recommend this for novices, especially if precision positioning is required. For your "sweep hand" timing application, I don't think micro-stepping will be necessary.
BTW, it looks like your chosen synchronous motor, if it's like the one I posted in post #15, can be operated with either a clock-wise or a counter clock-wise rotation. That hardly seems necessary, but it is what it is. You can purchase, online, geared-down 1 RPM clock motors that rotate in just one (non-reversable) direction, but I would avoid any eBay sellers, especially those based in mainland China, unless you KNOW the seller is reliable. It's always a crap-shoot ordering online, even from Amazon, although their return policies are usually generous.
If you want to explore using a stepper motor, go ahead and purchase a small motor (
NEMA 17 size is probably large enough), a PWM motor controller, and a low-voltage DC power supply. I, or someone else here in the forums, will help you get it working. If you need help selecting these components, I can help with that too. Unfortunately, someone who actually lives in Australia can probably steer you better than I can on the opposite side of the world.
Again, my BEST advice is to purchase a synchronous motor that actually produces 1 RPM when you connect it properly to 220 VAC 50 Hz "down under" power. Any other approach will be an adventure.
"I dont reckon it would have the torque (even if i balanced the second-hand - wind would blow it :-( )." You abosopositively MUST balance the seconds hand! I suggest carefully making it from Lexan (polycarbonate plastic) and then trimming the balance, perhaps with lengths of 50-50 plumbing solder wrapped around the seconds hand. Or drill a matrix of small holes to balance it. Maybe thread some wire through the holes to "fine tune" the balance.