You can try looking up the drive's official specs. But WD has been rather obtuse about RPM ever since they put out the green drives and claimed they were 5400-5900 RPM (they were all 5400 RPM except a few which were 5900 RPM).
For a non-invasive way to determine RPM, there are two ways:
1) Get HD Tune and run it on your drive.
http://www.hdtune.com/
The yellow dots in the graph correspond to how long it takes to read a random sector from the drive. This is the time to move the read/write heads from one track to another, plus the time for the correct sector to rotate underneath the head. Left-to-right is the time to move the read/write heads (left is smallest movement, right is furthest movement and thus greatest delay). The minimum wait time (bottom of the swath of yellow dots) is when the correct sector rotates under just as the heads arrive on that track. The maximum time (top of the swath of yellow dots) is when the platter has to complete a full rotation before it arrives under the heads.
Consequently, the vertical spread between a column of the yellow dots corresponds to the time it takes for the platters to complete one rotation.
A 7200 RPM drive takes (60 sec/min) / (7200 rev/min) = 0.0083 sec/rev = 8.3 milliseconds
A 5400 RPM drive takes (60 sec/min) / (5400 rev/min) = 0.0111 sec/rev = 11.1 milliseconds
2) Run a Fourier transform on the sound coming from the drive to generate a frequency spectrum graph. (You don't need to know how to program a Fourier transform. Lots of audio software can do it for you and generate a frequency spectrum.)
A 7200 RPM drive will have a sound spike at (7200 cycles) / (60 seconds) = 120 Hz.
A 5400 RPM drive will have it at (5400 cycles) / (60 seconds) = 90 Hz.
http://www.silentpcreview.com/article786-page2.html