my computer randomly shuts down

The loading bar is normal. It replaces the old spinning gear. For the other problem:

Reinstalling OS X Without Erasing the Drive

Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.

When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.

Reinstall OS X: Select Reinstall OS X and click on the Continue button.

Download and install the 10.10.1 update.

Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.

Also see:

Reinstall OS X Without Erasing the Drive

OS X Yosemite- Reinstall OS X

Note: You will need an active Internet connection. I suggest using Ethernet

if possible because it is three times faster than wireless.

OS X Yosemite: If your Mac restarts and a message appears

Reinstalling the operating system may or may not solve the problem, but it would be beneficial to determine what's causing the spurious shutdown events. Otherwise you may never determine the cause, and undiagnosed problems tend to repeat themselves until you do. I suggest the following.

Open the Console app - it's in your Mac's Utilities folder. If the log list column on the left is not already displayed, show the log list by selecting Show Log List from Console's View menu. Select Show Toolbar if it is not already shown.

Expand the "reveal triangles" in the left column adjacent to User Diagnostic Reports and System Diagnostic Reports. Find the most recent crash report which ends with the suffix .crash. Copy the text of that report and post it in a reply.

Other log files include kernel panic reports. They end in the suffix .panic. If you find one post it also.

Locate system.log in the list and select it. Many date and time-stamped entries will appear, hundreds of them, and you must find the entries relevant to your Mac's problem. If you type the words shutdown cause in Console's Filter field, it will show the log entries along with a numeric value representing the reason for the previous shutdown. The meaning of the code itself is not publicly known, but a negative code is understood to be an abnormal shutdown and possibly indicative of a hardware fault. The code itself may not be valuable, but the log entries that preceded the shutdown event may be helpful. If you want to copy and paste them in a reply, delete or obscure any information that you may consider personal (such as your Mac's name).

Yes. The negative code is understood to be an abnormal shutdown and possibly indicative of a hardware fault. Make a Genius Bar reservation to have it evaluated:

Genius Bar Reservations

The only way to test all memory already installed on the system performing the test is to use Apple Hardware Test / Apple Diagnostics. Its limitation is that the system is obviously constrained to function within its design specification, and therefore can't test for any conditions beyond that.

In other words it is possible for the installed RAM to pass AHT only to fail later, when some environmental parameter (usually, temperature) changes. If RAM fails AHT though, it's certainly bad and should be replaced.

Macs produced prior to June 2013 use Apple Hardware Test. Later Macs use Apple Diagnostics.

Memory Test

Memory Test (2)