Initially, a rod of mass [{mathjax fullwidth='false' m }] and length [{mathjax fullwidth='false' l }] moves without rotation on a frictionless surface in a direction perpendicular to the rod. the speed of the rod is [{mathjax fullwidth='false' v }]. at time [{mathjax fullwidth='false' t= 0 }], one end of the rod collides with (or brushes over) a fixed object. just after the collision, the rod is still parallel to the rod before the collision and the center of the rod still moves in the same direction as before. but the speed of the center of the rod is reduced to [{mathjax fullwidth='false' \frac{3}{4} v }]

a) find the angular velocity [{mathjax fullwidth='false' \omega }] of the rod just after the collision.
b) find the total kinetic energy of the rod after the collision.
c) find the speeds of the two ends of the rod just after the collision.