On average, both arms and hands together account for 13% of a person's mass, while the head is 7.0% and the trunk and legs account for 80%. We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 70.0 kg skater is 1.70 m tall, has arms that are each 70.0 cm long (including the hands), and a trunk that can be modeled as being 35.0 cm in diameter. If the skater is initially spinning at 84.0 rpm with her arms outstretched, what will her angular velocity w, be (in rpm) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble. rpm

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A horizontal vinyl record of mass 0.0855 kg and radius 0.101 m rotates freely about a vertical axis through its center with an angular speed of 4.18 rad/s and a rotational inertia of 2.64 x 10-4 kg·m2. Putty of mass 0.0253 kg drops vertically onto the record from above and sticks to the edge of the record.What is the angular speed of the record immediately afterwards?

The figure above shows Einstein spinning on a platform. He is initially spinning at a rate of 1rev/s, and holding his hands a distance of R1 = 80.3 cm away from his body. He then pulls his arms in to a distance of R2 = 40cm, changing his rotational speed. In this problem you can model Einstein’s body as a cylinder with a moment of inertia I = 30MR2, where M is his mass (60kg), and R is the distance his hands are from his body. (Notice that the figure shows him holding weights, but we are going to assume they are massless, to make it simpler!)(a) If he draws his arms in very quickly, you can safely ignore any frictional force on the platform. Assuming this is true, how fast is he rotating after he draws his arms in? (b)  In reality, after he draws his arms in friction will start to slow him down. If this small amount of friction is applying a torque of 4 Nm to the platform, how long would it take before Einstein stops moving?