Motor is idling rough.
Losse wheel, worn bearing, or more than likely, a worn CV joint.
Check your power steering fliud, if it is low this could cause the vibration you are feeling.
maybe the car need to be linged up n check the power steering.
The "awful grinding sound" might be a problem with your power steering
Not surprisingly, it depends, if the steering wheel vibrates all the time, no. IT could be a whole bunch of things. If it just vibrates at a certain speed range, roughly 50 to 70 mph, it is probably the tracking on your tires (or at least that's worth checking as it is a cheap procedure). Either way, if it makes you feel unsafe whilst driving the car, then don't drive it.
I have the same problem with my '91 Dodge Caravan -- it is probably the transmission.
A person removes the steering wheel with a steering wheel puller, after removing the airbag to the car. Then they put the new steering wheel on the car, after aligning it correctly.
Most likely the wheels and tires are not properly balanced... could also be something loose in front suspension.
Kinetic Energy helps the car wheel spin...
A wheel alignment is what syncs your steering wheel with your wheels. It ensures your car will drive straight when your steering wheel isn't turned.
Your ignition switch crapped on you
A car's steering wheel will vibrate when driving if the car's alignment needs to be adjusted.