Most likely your mac is having some software issues. This is usually fixable.
Take a look at Applications > Utilities > Console. This should contain a log of what happened when your mac froze. There might be clues to what the problem is.
BTW, you don't need to plug your iPad in to sync it. You can sync it with wifi.
Anyway, here are some basic troubleshooting and maintenance maneuvers to get you started:
1. Back up your hard drive first.
2. Make sure you have enough free space on your hard drive. Like 20 - 25%.
3. Repair permissions with disk utility, Disk Utility - Using Disk Utility to Repair Permissions
4. Boot into the recovery partition and repair your hard drive. OS X: About OS X Recovery
5. Make a new test user account and see if the problem is still present. Isolating an issue by using another user account
6. Try booting in safe mode and see if the problem is still present. OS X Mountain Lion: Start up in safe mode
This should keep you busy for a while.
Message was edited by: arthur