A uniform rod of mass M and length `l` is hinged at point O and is free to rotate on a horizontal smooth surface. Point O is at a distance of `(l)/(4)` from one end of the rod. A sharp impulse `P_(0) = 2 sqrt(130) kg m//s` is applied along the surface at one end of the rod as shown in figure `[tan theta = (9)/(7)]`
(a) Find the angular speed of the rod immediately after the hit
(b) Find the impulse on the rod due to the hinge.

Answer

(a) `omega = (36P_(0) cos theta)/(7ml) = (36)/(mL)`
(b) `P = P_(0) sqrt(sin^(2) theta + ((2)/(7) cos theta)^(2)) = sqrt(85 )N- s`