Will adapted UK Dual t/t play OK in USA?

I'm English and currently live in the USA. When I moved from the UK, I brought a UK floor lamp with me and use a mains step-up/down transformer that I purchased over here to run it.

I also have a mint 220/240V Dual CS 505-2 turntable in storage back home in the UK that I'd like to gift to a good friend over here, and wondered if it would play properly if I used it with the same transformer that's adapting my floor lamp?
Possibly not without a mod. Since the UK runs at 50 Hz I suspect you will find the TT turns too fast in the USA (there may be a change needed to the wheel size or gears that drive the wheel that drives the belt)