a) $\omega_p = \dfrac{-I_w \omega_w}{I_p}$
b) $\omega_p = \dfrac{-I_w \omega_w \cos{60}}{I_p}$
c) $\omega_p = \dfrac{I_w \omega_w}{I_p}$
d) the person will stop since the total angular momentum must be zero