HW#28 Ch 10: Rotation
Instructions: Be sure to write formulas and show substitutions to earn full credit.
1. Yuna Kim is a decorated South Korean figure skater who won the gold medal in the Vancouver Olympics. When she does a triple toe loop jump, her center of mass undergoes a change in height of 0.60 meters. If she completes 2.75 revolutions while in the air, what is her average rotational speed in radians per second? Hint: What is her total time in the air?
2. Sven Kramer, from the Netherlands, won the gold medal in the men’s 5000 m speed skating competition in the 2010 Winter Olympics. He skated 12 ½ laps in 6 minutes and 14.60 seconds, with an average speed of 13.40 m/s (30 mph) throughout most of the event. If the track is assumed to be circular (in reality it is shaped like an oval) and if Sven accelerated uniformly from rest up to an angular speed of 0.211 rad/s and traveled at constant angular velocity thereafter, for how long would he be accelerating? Use his total time along with equations with angular variables to solve this problem. Use the 12 ½ laps rather than the 5000 m to solve the problem.
3. A camel spin is a figure skating maneuver where the free leg is extended behind the body at hip level, parallel to the ice surface (see figure below). Assume that the leg of a male adult is composed of two cylinders stacked together representing the upper leg and lower leg/foot. One end of the upper leg is placed at the rotation axis. The upper leg (thigh) is a cylinder with mass 7.50 kg, length 63.3 cm and radius 5.99 cm, and the lower leg is a cylinder with mass 4.58 kg, length 57.6 cm and radius 4.82 cm. Assume the torso is a cylinder with mass 37.28 kg, length 62.5 cm and radius 13.58 cm, with one end placed at the rotation axis. Assume the head is a sphere with mass 6.07 kg and radius 10.93 cm, centered 81.7 cm from the rotation axis. Each arm is a horizontal cylinder with a mass of 3.75 kg, length 87.5 cm and radius 3.51 cm, with the rotation axis 62.6 cm from one end of each cylinder. What is the moment of inertia of a human male doing a camel spin?
4. Four point particles are connected by rigid massless rods in the shape of a square, with coordinates (0,0), (2,0), (2,2) and (0,2) for particles A, B, C, and D, respectively. All distances are in meters. If the particles have mass mA = 1 kg, mB = 2 kg, mC = 3 kg, and mD = 4 kg, and the rotation axis passes through the center of the square in a direction out of the page, what is the moment of inertia of the system of particles?
