What counts as child abuse?

I am 15 and I am not the genius my parents expect me to be. I do live in a Christian home but everything my dad is too lazy to handle he throws on me. If I do something wrong like lets say argue with my sister (which in my opinion happens between every pair of siblings on the face of the earth) and today my dad wanted my sister to return mail something and he gave her a box with some random shipping paper stuff in it and told her to ask me about it. She asked me in a polite way and he called her back and told her to do it over again in a more polite way. So she did and we sorta laughed about it, cause I mean it was sorta funny. So i looked through the papers and couldn't figure it out because it was all just about how to activate the product that was recieved and there was no return paper stuff or anything just some stickers with adresses on them and no clear reason for them. So i told her to take it back to him because i dont understand what to do with it. He called me over with a long plastic/flimsyish stick in his hands and told me to bend over i asked why and he told me that I didn't listen to him. I told him to just let me explain (what i said above) and he said okay ima hit you twise now and i start balling because he didn't give me a chance to explain and then he hits me. The marks stay there for a week or so. I asked my mom why she didn't stand up for me and she said because it doesn't matter and i said isn't it child abuse or something because he hit me because i didnt know something??? And she said no because all my friends get "spanked" and the friend she refered to was a druggy.. I dont know if this is child abuse or just a normal family being disiplned. My dad hasn't "spanked" (in my moms words) me in 2 years but my little brother and sister get hit alot. We are also going through a hard time as a family right now we got 30 days notice that we have to be out of our house and my dad lost his job. Also he yells at me alot. I have some music with cuss words in it but what 15 year old doesn't he hear **** in one of them and threatened to take away my music privileges. I mouthed off and he started telling me im untrustworthy and he was gonna treat me like im a kid again. He knows that people trusting me is one of the biggest things that matter to me and i was balling after he said that, and this all sounds stupid and pointless.... I admit i do have a mouth on me and i know he would hit me more if i didnt keep my distanse. he wants me to have a better relationship with him but everytime i try he finds something wrong and he is mad about it for weeks... help please to clear up weather or not i should be worried about this!