Conservation of Angular Momentum During a jump to his...

Conservation of Angular Momentum During a jump to his partner, an aerialist is to make a quadruple somersault lasting a time $t=1.87$ s. For the first and last quarter-revolution, he is in the extended orientation shown in Fig. $11-55,$ with rotational inertia $I_{1}=19.9 \mathrm{kg} \cdot \mathrm{m}^{2}$ around his center of mass (the dot). During the rest of the flight he is in a tight tuck, with rotational inertia $I_{2}=3.93 \mathrm{kg} \cdot \mathrm{m}^{2} .$ What must be his angular speed $\omega_{2}$ around his center of mass during the tuck?

Conservation of Angular Momentum
During a jump to his partner, an aerialist is to make a quadruple somersault lasting a time $t=1.87$ s. For the first and last quarter-revolution, he is in the extended orientation shown in Fig. $11-55,$ with rotational inertia $I_{1}=19.9 \mathrm{kg} \cdot \mathrm{m}^{2}$ around his center of mass (the dot). During the rest of the flight he is in a tight tuck, with rotational inertia $I_{2}=3.93 \mathrm{kg} \cdot \mathrm{m}^{2} .$ What must be his angular speed $\omega_{2}$ around his center of mass during the tuck?

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Key Concepts

Conservation of Angular Momentum

This principle states that in the absence of an external torque, the total angular momentum of a system remains constant. In rotational dynamics, if the moment of inertia changes due to a change in body configuration, the angular speed adjusts in such a way that the product of moment of inertia and angular velocity stays the same.

Moment of Inertia

This is a measure of an object's resistance to changes in its rotational motion around a given axis. It depends on both the mass and the distribution of that mass relative to the axis of rotation. Variations in body posture, such as extending the limbs or tucking, can lead to significant changes in the moment of inertia.

Angular Velocity

Angular velocity refers to the rate at which an object rotates about an axis. When the moment of inertia decreases due to a change in body configuration (like tucking), conservation of angular momentum requires that the angular velocity increases correspondingly, allowing the performer to complete rotations more rapidly.

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