A wheel $($mass m$1=0\mathrm{.}8[$kg$],$ radius r$=0\mathrm{.}4[$m$])$ is initially at rest on the middle of a flat slab $($mass m$2=8[$kg$],$ length $=2\mathrm{.}4[$m$])$ when a sudden horizontal $12[$N$$s$]$ impulse due to force P $($to the right$)$ is applied to the slab over a very short time interval. The wheel's radius of gyration about its mass center $($which is also its geometric center$)$ is kG$=0\mathrm{.}2[$m$].$ The wheel does not slip on the slab, but friction between the slab and the flat horizontal ground surface is negligible.

Find vG after the impulse is applied. Assume the slab does not tip and just slides horizontally. Assume positive is to the right when reporting your answer for vG$.$

Find:

a$)$ $2,$ the pendulum's angular velocity just before impact; and

b$)$ $3,$ the pendulum's angular velocity just after impact.

Consider counterclockwise as positive when reporting your answers for angular velocities.