I need lower gears because I pull a bike trailer with 2 kids in it, and it gets hard going up hills. Especially since I'm not in shape or an experienced cyclist. My highest tooth count sprocket in my cassette is 28 tooth. The guy at the bike shop told me that 28 tooth is the highest you can get in a 7 speed cassette, But I have found as high as 32 and 34 tooth online. I assume he knows what he's talking about so I have doubts that what I'm finding online will work. My cassette is a shimano hyperglide.
I am also confused about the chain that I should buy. The old chain (original, from 1992) says CN-UG50. In a description of the cassette I came across, it says nothing about UG50, but it does say that it's not compatible with IG50, and I'm not sure if that's the same. What chain should I buy that is a replacement for my original chain. I did find the UG50 which is supposedly obsolete; will it work? Is there something better?
You can use any chain that is 7 or 8 speed and Shimano Hyperglide compatible. The "iG" is "Interactive Glide", and is kind of its own thing that Shimano did in the late '90s.
The biggest problem you may face is that your rear derailleur may need to be changed for one with a longer cage (the arm/pulley assembly that hangs down below the cassette) to allow it to work with a cassette with such a large gearing range. I think your bike shop guy is just ignorant of what's available.
There are a couple Shimano HG chains on that page (HG50 and HG70), and a SRAM PC-830 that would work great, and a couple of the KMC options would probably work, too. Personally, I'd stay with a Shimano chain since you want a cassette with a huge jump in gearing (makes for difficult shifting if not set up properly--having chain and cassette from the same manufacturer will help to that end).
I need lower gears because I pull a bike trailer with 2 kids in it, and it gets hard going up hills. Especially since I'm not in shape or an experienced cyclist. My highest tooth count sprocket in my cassette is 28 tooth. The guy at the bike shop told me that 28 tooth is the highest you can get in a 7 speed cassette, But I have found as high as 32 and 34 tooth online. I assume he knows what he's talking about so I have doubts that what I'm finding online will work. My cassette is a shimano hyperglide.
The MAIN (?) thing which you need to ensure is that your bike's rear wheel uses a Cassette (as you presume) and not a Freewheel ...
as jpr95 suggested, there may-or-may-not be an issue with your bike's current rear derailleur being able to accommodate a 34t cog ... most Shimano rear derailleurs CAN, but some cannot.
Personally, I would presume that the guy in the bike shop does NOT know what he is talking about if he tells you something which is so obviously contradictory to what you have discovered through your online research.
If there is another bike shop (or, an REI) within 16 miles of where you live, you may want to go there in the future.
The chain looks narrow enough. It looks like an 8-speed, which works fine with 5-, 6-, and 7-, too. The question is, is it long enough? And the other question is will the cassette work with your rear derailleur? Can't make a diagnosis without seeing the patient.
