a slender rod CD of length (l) and mass (m) is placed upright on a motionless horizontal surface . a second identical rod AB is moving along the surface with a velocity (vt) when its end B strikes squarely the end C of the rod CD . if the coefficient of restitution between the rods is e=0.5, determine the velocity of the rod AB, the angular velocity of the rod CD , and the velocity of the c.o.m. of rod CD.
24AB
v(initial)=v
v(final)=v1
CD
v(final)=v2
First of all ,conserve linear momentum
mv=mv1+mv2 -----------------(1)
Consider both rod as system => No torqu on system => ANgular momentum conserved
=> mvl/2 =mv1 l/2 + mωl2/12 ----------(2)
Applying coeff of restitution eqn
=> -e = (v2+ωl/2)-v1 / 0-v -----------(3
solve (1),(2),(3) to get ans
