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We propose a new configuration for realizing torsional optomechanics: an optically trapped windmill-shaped dielectric interacting with Laguerre-Gaussian cavity modes containing both angular and radial nodes. In contrast to existing schemes, our method can couple mechanical oscillators smaller than the optical beam waist to the in-principle unlimited orbital angular momentum that can be carried by a single photon, and thus generate substantial optomechanical interactions. Combining thedoi:10.1080/09500340.2013.778341 fatcat:smwli36gvrdgpnchbrotjrd2sy