Solution
= Solution
Differentiate $\mathcal G=\sum_i\mathbf p_i\cdot\mathbf r_i$:
$$
\dot{\mathcal G}=\sum_i(\mathbf F_i\cdot\mathbf r_i+\mathbf p_i\cdot\dot{\mathbf r}_i)
=\sum_i\mathbf F_i\cdot\mathbf r_i+2T.
$$
= Solution
Differentiate $\mathcal G=\sum_i\mathbf p_i\cdot\mathbf r_i$:
$$
\dot{\mathcal G}=\sum_i(\mathbf F_i\cdot\mathbf r_i+\mathbf p_i\cdot\dot{\mathbf r}_i)
=\sum_i\mathbf F_i\cdot\mathbf r_i+2T.
$$