Difficult Riddles

You write on me and secrets I can keep;
In places never seen, I spin like a top;
Though stiff as a board, I’m often described like a mop.
What am I?
Answer - a floppy disk.

Take away my first letter and I am unchanged;
Take away my second letter and I am unchanged;
Take away all my remaining letters and I am still unchanged!
What am I?
Answer - The postman or a mailbox.

Jenn picked a book off the highest shelf in her room. On the spine she read How to Jog. She ran out of the room and opened the book but found it had absolutely nothing to do with jogging.
Explain…….
Answer - The book Jenn picked up was one of a set of encyclopedias; she picked up the volume containing entries beginning with the letters “HOW” through the letters “JOG”.

What is that which goes with a car, comes with a car, is of no use to a car, and yet the car cannot go without it?
Answer - Noise.