it sounds alot like a wheel balance is needed....
parking brake on.
During acceleration? I'm not sure. But when both idling and acceleration the engine's combustion can cause a lot of vibration in the steering wheel if you are in an older vehicle.
The vibration was so severe in the front end, I had trouble steering the car. I could only feel the vibration when the car accelerated. Earthquakes cause a distinct vibration of the earth.
More than likely a tire out of balance, or a tire with a defect. The tyrod end may also be the culprit.
Steering wheel vibration when applying brakes is usually caused by warped disc brake rotors
Tire out of balance is the most likely cause. Have the tires/wheels inspected, rotated, and balanced.
Warped rotor,Tie rods, Wheel bearings (hub).
The most common cause is a tire out of balance. It can also be a bent wheel, defective tire, wheel bearing, or steering parts worn.
Tires can be either out of balance or have a slipped belt and cause vibration in the steering wheel. Wheels can be bent and cause it. CV joints can be almost to the point of failure and cause it. Excessively loose steering components (ball joints, Rack, idler arm (if present), struts... Either the front or rear drive shafts could be out of balance most likely the front
I would suspect a tire out of balance. Have your tires balanced and see if it goes away.
This is probably due to worn brake rotors on the brakes, if there is no vibration when driving then this will be the cause.
Vibration when applying brakes is most likely warped rotors. Another cause could be loose caliper bolts. The vibration while driving is most likely a tire issue ie (out of balance, broken belt in tire, bent rim). Other possible causes are loose/worn suspension and/or steering parts.