A yoyo is a toy made of three uniform density disks with a string wrapped around the middle disk. The middle disk has a mass m and radius ; the outer disks each have mass and radius . The string has negligible mass and stretches a negligible amount. Analyze the following situation. As the yoyo is moving downward, you pull up with a constant force F and as you pull, your hand moves upward a distance . At the beginning of your move the yoyo was headed downward with speed 1 and angular speed 1. When your hand has moved up a distance , the yoyo has moved down a smaller distance ℎ and has speed 2 downward and angular speed 2. Assume that the string doesn't slip or rub against the outer disks, so there is no change in temperature of the yoyo. a. The moment of inertia of the yoyo is the sum of the moments of inertia of the three disks about the axis of rotation. Calculate this quantity.
b. Calculate the speed 2.
c. Calculate the angular speed 2.

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?