Why my rear brakes/wheels make weird noises?
 

I was rear ended by a truck while my hand brake was up. The truck pushed my car only about 3 feet and the damage was only done to the rear bumper and spoiler. I got them fixed but ever since the accident, I noticed immediately that there is a noise coming from my rear wheels.

Sounds like a vibration cracking sound from the driver side rear wheel. I also noticed that when I put my hand brake on and I jack up the car to remove the wheel, the handbrake is supposed to hold the wheel in place while I unbolt it, right?

When I unbolt it, the torsional force actually moves the wheel easily about 3-4 inches rotationally before the hand brake actually holds the wheel in place.

The sound is most noticeable at low speeds in 2nd gear or neutral around 20-30mph. It is an intermittent sound that happens about twice per day driving 20 miles per day. The noise lasts until I speed up or slow down to 10mph. My exhaust is loud so it is possible that the noise is still there at higher speeds.

A separate noise also happened after accident on the rear right wheel(Passenger side) At random times/speeds under 35mph, the rear wheel starts vibrating A LOT. The entire car shakes and the noise is loud from that rear wheel and I hear a bunch of metal clunking together. This happens about 3 times per week and lasts about 5 seconds.

Mechanics don't see anything wrong visually. I have since then autox'ed the car and tracked it. The suspension and handling feels great on the track. No signs of problems.

I know the noise of a wheel bearing and the noise of bad brakes so I know that is not the problem. I checked the wheel bolts. They are all tight.

Is it a possibility the accident may have been so severe it damaged the motor mount from the engine & transmission jolting forward? You should also take a look at the transmission mounts to see if any green/bluish fluid leaked out. As for the motor mount it's impossible to tell without taking the assembly out, so I could see if the mechanics could not see anything visually wrong. If you've exhausted all your options you may just try that. I don't like giving such a suggestion but the symptoms described can be mount, and a collision could easily damage such component.

You should remove your rear rotors to inspect the parking brake shoes & springs. The springs are not cheap so I would inspect 1st before buying new parts.

+1. This would be far more likely than what I said earlier. Especially on the rear wheel that is vibrating.

I have read somewhere before a long time ago that the rear brakes are weak and they cannot be used to initiate a drift without breaking them.

I will take it apart sometime to check it out. It is definitely not a motor mount.

Correct, the hand brake will not hold enough to brake lose some bolts. Air tools are no problem. The rear shoes are very small and are suppose to be used in connection with transmission.