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tires are made of rubber and rubber can cause friction
No. That would be friction.
In general rolling friction is any friction specifically related to the rolling motion. The friction on the axle to hub bearing, the tire flexing, the tire tread on the surface of the road and so on.
Friction or grip if it's friction i think the tyre with the most contact with the road surface. If it's grip then the one with the tread
heat
A worn tire reduces friction and tracktion, this could be dangerous in bad weather conditions., A2 A worn tyre would actually improve friction in dry conditions, because the surface area touching the road, will be greater without tread. This why racing cars use 'slicks' in dry conditions. The problems arise in wet weather. The thinnest film of water between the tyre and the road, will cause a sudden decrease in friction, 'aquaplaning'. The tread is there purely for wet conditions.
When the tire tread wears down to the wear bars, the tires are ready for replacement.
The large chunk of tire tread may have ripped the wires off a O2 sensor.
CV Joints? Rocks in the tire tread?
when the tread is worn down to 1/16 inch
It is an indicator of tire tread wear.
It does not! In fact will DEcrease contact and therefore friction. A bald or smooth tyre will be best on dry surface. The purpose of tread on tyres is to sipe away water on wet road and a rough tread would act in similar manner though far less efficiently.