Physics : Dual Rotation..........

Initially w=v/r

Ei=mv²

finally... w doesnot changes.. but v becomes v/2 (in forward direction and momentum conservation...)

v in upward direction=0(max ht)

so mv²=mgh+1/2m(v/2)²+1/2m(v/2)²+1/2mr²w²
mv²=mgh+1/2m(v/2)²+1/2m(v/2)²+1/2mv² .w=v/r

so h=v²/4g

Q.112

writing about com

Il/2=ml²/12ω

also I=mv_c

given ωl/2-v_c=v

solving these we get

ω=6I/ml

6I/ml(l/2)-I/m=v

I=mv/2... answer

1/2(mv²)+1/2(mr²)(v/r)²=mv²