Problem 7.163 Challenge

จาก \(Σ\vec{L}_{f}= \Sigma \vec{L}_{i}; \Sigma τ = 0\)

\(|\Sigma \vec{L}_{f}|= |\Sigma \vec{L}_{i}|\)

\(I_{f}\omega _{f}= rp_{i}\)

\((m(\frac{\ell}{2})^{2}+\frac{1}{12}M\ell ^{2})\omega _{f}=(\frac{\ell}{2})(mu)\)

\(\omega _{f}=\frac{6mu}{(3m + M)\ell}\)

จาก \(\Delta K = K_{f}- K_{i}\)

\(\Delta K=\frac{1}{2}I_{f}\omega _{f}^{2}-\frac{1}{2}mv_{i}^{2}\)

\(\Delta K=\frac{1}{2}(m(\frac{\ell}{2})^{2}+\frac{1}{12}M\ell ^{2})(\frac{6mu}{(3m + M)\ell})^{2}-\frac{1}{2}mu^{2}\)

\(\Delta K = -\frac{mMu^{2}}{2(3m + M)}\;\blacksquare\)