By bringing her arms and knees close the diver decreases her moment of inertia and increases her angular velocity.
The law of conservation of angular momentum states that if no external torque acts on a body, the angular momentum remains constant.
[tex] L=I\omega [/tex]
the moment of inertia of the diver is I and ω is his angular velocity.
When the diver makes a somersault, she rotates her body about an axis perpendicular to the plane of his body.
The diver can be considered to be made of particles of different masses [tex] m_1,m_2,...m_n [/tex]situated at distances[tex] r_1,r_2,...r_n [/tex] from the axis of rotation.
[tex] I=\Sigma mr^2 [/tex]
If the diver jumps and makes the dive at an angle, she has a certain value of initial angular momentum. During the period in which the jump is made, no external torque acts on her, and therefore, her angular momentum during the dive remains constant.
[tex] I\omega = constant\\
I_1\omega_1 =I_2\omega_2 [/tex]
When she brings her arms and knees together, her moment of inertia reduces, since the distances of her arms and knees from the axis of rotation decreases.
Since
[tex] \omega \alpha \frac{1}{I} [/tex]
her angular velocity increases and she is able to spin faster and complete the somersault.
