Does the car vibrating at stop lights have anything to do with white smoke coming out of tailpipe?

It's unlikely that the car vibrating at stoplights is *directly* caused by the white smoke from the tailpipe, but both could be symptoms of a related underlying problem. White smoke usually indicates a coolant leak into the combustion chamber or exhaust system. The vibration at idle could be due to a number of things, but some of these could be related to the coolant leak.

Here's a breakdown:

* White smoke (coolant leak): This suggests a serious problem. The coolant is entering the cylinders and being burned, resulting in white smoke. The source could be a blown head gasket, cracked engine block, or a failing cylinder head.

* Vibration at idle: This can be caused by many things, including:

* Misfire: A failing ignition system, faulty spark plugs, or low compression in one or more cylinders (which *could* be related to a coolant leak causing damage) can cause misfires and vibrations.

* Engine mounts: Worn engine mounts can allow excessive engine movement, leading to vibrations.

* Transmission issues: Problems with the transmission can sometimes cause vibrations felt at idle.

* Unbalanced engine components: Internal engine damage (like from a coolant leak damaging components) can lead to vibrations.

The connection: The crucial point is that a significant coolant leak (causing the white smoke) *could* lead to internal engine damage that then manifests as vibrations at idle. The leak might cause damage to the cylinder head, piston rings, or other components, disrupting the smooth operation of the engine and leading to vibrations.

In short, while the vibration isn't directly *caused* by the smoke, both are symptoms that suggest a serious underlying mechanical issue, likely related to a coolant leak, which needs professional diagnosis and repair immediately. Continuing to drive the car with a coolant leak can cause catastrophic engine damage.