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Yesterday I bought an -98 with M6, when I start the car and push the clutch and put the 1st gear, after taking off it smells burnt clutch why. It´s not the first time I drive an Manual car and the other cars dont have these smell.
And is it a common problem with cracking front rotors? How much do they cost?
The Corvette clutch is pretty resilient. I would recommend having the clutch examined to see if it is glazed or truly smoked. A lot of people drive these cars really hard and "exercise" the clutch as a result. You should never have a burnt clutch smell as a routine.
Cracked rotors on stock are virtually unheard of. Some aftermarket drilled rotors crack at the drilled holes. If you have the solid OEM rotor you should never have any cracks. Some people think that turning a rotor is proper maintenance and will turn a rotor down to the point where it is too thin. It's an easy - but not inexpensive - fix. Simply replace the rotors.
Both of the problems you have described are easily repaired and would cost around $1200-$1400 US to do at a dealership. Keep the car. You'll love it.
You shouldn't have any clutch smell if it is working properly. Sometimes you will get a smell if you are slipping it when starting from a red light on a hill or maybe caught the wrong gear, but those are instances when the clutch is burning because it is slipping and not fully engaged.