  We invoke star formation triggered by cloud-cloud collisions to explain
global star formation rates of disk galaxies and circumnuclear starbursts.
Previous theories based on the growth rate of gravitational perturbations
ignore the dynamically important presence of magnetic fields. Theories based on
triggering by spiral density waves fail to explain star formation in systems
without such waves. Furthermore, observations suggest gas and stellar disk
instabilities are decoupled. Following Gammie, Ostriker & Jog (1991), the cloud
collision rate is set by the shear velocity of encounters with initial impact
parameters of a few tidal radii, due to differential rotation in the disk.
This, together with the effective confinement of cloud orbits to a two
dimensional plane, enhances the collision rate above that for particles in a
three dimensional box. We predict Sigma_{SFR}(R) proportional to Sigma_{gas}
Omega (1-0.7 beta). For constant circular velocity (beta = 0), this is in
agreement with recent observations (Kennicutt 1998). We predict a B-band
Tully-Fisher relation: L_{B} proportional to v_{circ}^{7/3}, also consistent
with observations. As additional tests, we predict enhanced star formation in
regions with relatively high shear rates, and lower star formation efficiencies
in clouds of higher mass.
