Final answer:
The diver's rotational rate during a somersault with a rotational kinetic energy of 117 J and moment of inertia of 9 kg·m² is approximately 5.1 rad/s, calculated using the formula for rotational kinetic energy.
Step-by-step explanation:
The student is asking about the rotational rate of a diver during a somersault given the diver's rotational kinetic energy and moment of inertia.
To find the rotational rate, we can use the formula for rotational kinetic energy, which is K.E. = ½Iω², where K.E. is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity (rotational rate).
Given that the rotational kinetic energy (K.E.) is 117 J and the moment of inertia in the tuck position (I) is 9 kg·m², we can rearrange the formula to solve for ω: ω = √(2K.E./I). Substituting the values gives us ω = √(2 * 117 J / 9 kg·m²) = √(26) approximately equals 5.1 rad/s. Therefore, the diver's rotational rate during the somersault is approximately 5.1 rad/s.