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# Rotational Inertia: Resistance to Change in Rotary Motion (page 2)

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Author: Janice VanCleave

1. The center of mass of an object is the point at which the whole mass of an object is considered to be concentrated. This is the same as the center of gravity if the object is in a uniform gravitational field (the region of space in which a force of gravity acts on objects), such as that about Earth. The center of mass of a disk (a solid cylinder) is nearer its axis than is the center of mass of a hoop. Design an experiment to determine the effect of an object's center of mass in relation to its axis on the object's rotational inertia. Use objects with the same mass and shape but with different center-of-mass locations, such as two identical metal cans with lids and 10 metal washers. You will compare the rotational inertia of the cans by allowing them to roll down an incline. The can with the greater translational speed has less rotational inertia. Prepare the two cans by taping the washers inside (see Figure 9.2 on p. 64). Inside one of the cans, use thin strips of duct tape to secure five washers to the bottom of the can and five washers around the inside of the lid. In the second can, tape the five washers together in a pile and tape the pile to the center of the bottom of the can. Stack and secure five more washers and attach them to the middle of the inside of the can's lid. Put the lids on both cans. Place the cans together at the top of a ramp (this can be a board raised at one end). Release the cans simultaneously and allow them to roll down the ramp. Use the results to decide how the location of the center of mass affects rotational inertia.
2. Another way to determine how the center of mass of an object affects its rotational inertia is to use two 36-inch (90-cm) dowels and four equal masses of clay. Add one clay mass to each end of one dowel. Hold the dowel in the center and rotate it back and forth for about half of a turn. Note the effort required to turn the dowel and to reverse the motion. In this position, the clay masses are each 18 inches (45 cm) from the center of the dowel, which is its axis of rotation, so the center of mass of the dowel is at its greatest distance from the axis. With the clay in this position, the rotational inertia will be called I1. Place the remaining two clay masses around the second dowel at points 8 inches (20 em) closer to the center of the dowel, which will be 10 inches (25 em) from the center. In this position, the center of mass is closer to the axis. Rotate this dowel back and forth, as before, making a point to rotate it at the same speed as before. With the clay in this second position, rotational inertia will be called I2. Repeat, rotating each dowel several times to make a comparison. As the rotational inertia of the dowel increases, it is more difficult to rotate it. Which dowel is easier to rotate? In other words, is I1 greater than I2?

### Get the Facts

1. Cats can quickly spin and land on their feet if dropped from an upside-down position. How is the rotational inertia of the front and the back of the cat changed? How does this difference affect the landing position? For information, see P. Erik Gundersen, The Handy Physics Answer Book (Detroit: Visible Ink, 1999), pp. 75-76. Note: It is not suggested that you try this with a cat. It takes special photographic equipment to make the observation, and special care must be taken to keep the cat from being injured.
2. Newton's law of conservation of momentum states that an object in motion remains in motion unless it is acted upon by a net force. This means that a rotating object will continue to spin unless it is acted on by a twisting force in the opposite direction. How is angular momentum determined? How can conservation of angular momentum be used to explain why a skater spins faster when the skater suddenly draws his or her arms in? For information, see Paul Doherty, The Spinning Blackboard & Other Dynamic Experiments on Force & Motion (New York: Wiley, 1996), pp. 55-58.
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