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Rotational Dynamics Simple Harmonic Motion

A woman stands at the center of a platform. The woman and the platform rotate with an angular speed of 1.30 rad/s. Friction is negligible. Her arms are outstretched, and she is holding a dumbbell in each hand. In this position the total moment of inertia of the rotating system (platform, woman, and dumbbells) is 6.66 kg·m2. By pulling in her arms, the moment of inertia is reduced to 4.14 kg·m2. Find her new angular speed.

A thin rod has a length of 0.835 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.794 rad/s and a moment of inertia of 1.2 x 10-3 kg·m2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?

In preparation for shooting a ball in a pinball machine, a spring (k = 703 N/m) is compressed by 0.0780 m relative to its unstrained length. The ball (m = 0.0567 kg) is at rest against the spring at point A. When the spring is released, the ball slides (without rolling) to point B, which is 0.395 m higher than point A. How fast is the ball moving at B?

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From the conservation of angular momentum ...

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