We analyze the parity-violating (PV) components of the analyzing power in elastic electron-proton scattering and discuss their sensitivity to the strange quark contributions to the proton weak form factors. We point out that the component of the analyzing power along the momentum transfer is independent of the electric weak form factor and thus compares favorably with the PV beam asymmetry for a determination of the strangeness magnetic moment. We also show that the transverse component could be used for constraining the strangeness radius. Finally, we argue that a measurement of both components could give experimental information on the strangeness axial charge.
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