We study the modification of the atomic spontaneous emission rate, i.e.,the Purcell effect, of Rb-87 in the vicinity of an optical nanofiber (similar to 500 nm diameter). We observe enhancement and inhibition of the atomic decay rate depending on the alignment of the induced atomic dipole relative to the nanofiber. We present calculations with two different methods that qualitatively agree with some of the results; the calculations that best agree consider the atoms as simple oscillating dipoles. This is surprising since the multilevel nature of the atoms should produce a different radiation pattern, predicting different modification of the lifetime than the measured ones. This work is a step towards characterizing and controlling atomic properties near optical waveguides, fundamental tools for the development of quantum photonics.