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Reformat the disk to FAT32, which ( as suggested by Michael Sturm) is the lowest common denominator in file systems between OS X and Windows. This file system type is not natively supported by Windows, which is why the disk will not mount when you plug it into your laptop. If it is Mac OS Extended or a something similar then your disk is using the HFS+ file system, which is the default for OS X.
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the name you see in your file tree when the disk mounts under OS X) what do you see for the Format at the bottom of the window? If you open the Disk Utility application on your Mac with the disk connected, you should be able to see it in the list of disks on the left hand column of the Disk Utility window.
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