Answer:
θ₁ = 0.5 revolution
Explanation:
We will use the conservation of angular momentum as follows:
[tex]L_1=L_2\\I_1\omega_1=I_2\omega_2[/tex]
where,
I₁ = initial moment of inertia = 18 kg.m²
I₂ = Final moment of inertia = 3.6 kg.m²
ω₁ = initial angular velocity = ?
ω₂ = Final Angular velocity = [tex]\frac{\theta_2}{t_2} = \frac{2\ rev}{1.2\ s}[/tex] = 1.67 rev/s
Therefore,
[tex](18\ kg.m^2)\omega_1 = (3.6\ kg.m^2)(1.67\ rev/s)\\\\\omega_1 = \frac{(3.6\ kg.m^2)(1.67\ rev/s)}{(18\ kg.m^2)}\\\\\omega_1 = \frac{\theta_1}{t_1} = 0.333\ rev/s\\\\\theta_1 = (0.333\ rev/s)t_1[/tex]
where,
θ₁ = revolutions if she had not tucked at all = ?
t₁ = time = 1.5 s
Therefore,
[tex]\theta_1 = (0.333\ rev/s)(1.5\ s)\\[/tex]
θ₁ = 0.5 revolution