Question

B and C please

Answer 1

Moment of (nertia about kinse Io Iod +I ball M2 +M02 3 2Inital angulav mone tum aborut hinge Li MUDCoso Sappose final angu lay velocity is zwf then Ainal angu lay mometum using anulaY MOmentum Conservation we have MUD COS muD LoS CO wf

Hence,

part - b

The total moment of Inertia is

$\boxed{I = \frac{ML^2}{3} + mD^2}$

Part - c

The angular speed immediately after collision is given by

$w_f = \frac{mvD cos \theta}{\frac{ML^2}{3}+ mD^2}$

by plugging all the values we get

$w_f = \frac{(45 \times 10^{-3}kg)(5.86 m/s)(1.1m \times \frac{2}{3}) cos (48 ^\circ)}{\frac{(3.1 kg)(1.1m)^2}{3}+ (45 \times 10^{-3}kg)(1.1 m \times \frac{2}{3})^2}$

which gives us

$\boxed{w_f = 0.101525 rad/s}$