My iMac 27 inch is very slow seems to churn and the beach ball is showing

Question

I have an iMac 27" bought in 2010 3.2 GHz Intel core i# processor, 4 GB 1333 MHz DDR3 Memory,  1TB SATA disk.
It is running for a long time when starting up and the beach ball is showing several times. It can last for up to 45 minutes for all the processor noise to go down then it works fine until I open an application. It starts to run in the background again and everything slows down. At first it was the backup but that is not the case anymore. Could someone help me to speed this iMac up again.
Thanks
Abe

Answer 1

When you see a beachball cursor or the slowness is especially bad, note the exact time: hour, minute, second.  
These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
The title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above.
Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first.
Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Some private information, such as your name, may appear in the log. Anonymize before posting.