Hi Guys.
Ok - I have just bought a K1 GSXR 600, lovely bike and insanely fast compared to my SV

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However I am having a problem with the handling and was hoping someone might be able to help, I know a lot of people on here have now 'graduated' to gixers

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Bit of history - The bike has only done 3000 miles, though it is a 2001 model so is 6 years old. Tyres and chain all look to be ok. Tyre pressures checked - 36 and 42 psi. All suspension settings are stock and I weigh around 11 stone.
When riding in a straight line bike feels good, however as soon as try to turn the front end 'flops' into the corner. So, as an example, going round a roundabout, it feels as if the front wheel is flopping towards the roundabout, so I have to literally turn the handlebars to the left in order to hold the wheel in line with the back wheel!
One thing I thought might be causing it - I suspect as the bike has only done 3000 miles it has never had new tyres so those tyres could potentially be 6 years old!? Could that be the cause? They are Dragon Evos.
Thanks for any advice guys, much appreciated