The problem of impulsive spin‐up from rest of a fluid of kinematic viscosity &ngr; in a closed cylindrical container is examined numerically and experimentally. The shape of the velocity profiles is found to depend upon a parameter &agr;0=h(&ngr;/&OHgr;1/2/a2, wherehis the height, a is the radius, and &OHgr; is the angular speed of the container. When &agr;0is less than 0.005, the numerical profiles agree well with the solutions of Wedemeyer and Venezian, and the fractional spin‐up time (the time to reach some fraction of solid body rotation) is proportional toh(&ngr;/&OHgr;)−1/2. When &agr;0is larger than 1, the numerical profiles agree well with the solution of the diffusion equation, and the fractional spin‐up time is proportional toa2/&ngr;. For intermediate values of &agr;0, the numerical profiles agree well with experiment, and the dependence of the fractional spin‐up time on &OHgr;, &ngr;,h, andavaries with &agr;0, with radial positionr, and with the dimensionless angular velocityW=v/r&OHgr;, wherevis the azimuthal velocity.