2003 Rav 4 - Roaring in the rear

Possible wheel bearing that is worn. Have the bearings inspected.

Does it have a clutch fan or electric fan ? Clutch fans make a loud roaring noise when going bad.

Hi Linda
loud roaring noise means the wheel bearing failed and have to be change.
Good Luck

Harmonic balancer.

YOUR BREAKER SYSEM OR YOUR Bearings

A loud "roaring" noise as you describe it could very likely be a bearing going out.

Then noise you hear after shutting off the car very well might be the air suspension compressor. The air ride system is still activated for a half hour after the vehicle has been shut off. The roaring noise from the rear could be a bad bearing. The rear axle seals don't always leak when a bearing goes out. So it's not a conclusive indication that they are good just because the seals aren't leaking. If your mechanic isn't too versed in differentials it may be advisable to seek an opinion of a reputable transmission shop (however, that may be a difficult task).

That roaring noise should be a wheel bearing. Jack up the rear wheels and spin the tires by hand. You can hear a grinding noise if the noise inside the car is as load as you state.. The only other noise that will be like that is the differental gears inside the drive axle

check to see if loose first

One of the front wheel bearings are bad. Jack it up and see if one is loose, the noise will usually change if you swerve back and forth while driving. Could also be a rear pinion bearing in the rear axle.