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# Rotational Motion: Spinning Objects (page 2)

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Author: Janice VanCleave

### Try New Approaches

How do the translational speeds compare for other shapes? Repeat the investigation using different shapes, such as the following:

• a disk (a solid cylinder), such as an unopened can of solid food (tomato soup or cranberry sauce), or a dowel
• a hoop (a hollow cylinder), such as an empty can with the ends removed, or a cardboard tube

For each test, use two objects of the same shape but different sizes, such as two solid cylinders or two hoops.

1.
1. In the original experiment, the spheres differ in mass and size but have the same translational speed. Design a way to test the effect of only one of these factors, such as mass, on translational speed. Make sure that the only difference between the two objects is their weight. (Note that on Earth, a change in weight is a change in mass, with their relationship being 454 grams/1 pound.) One way to do this is to use two food cans of equal size but different weight. (You can use small, empty plastic cylinders with removable lids that can be filled with different solid materials, such as clay or sugar.) Using the ramp and procedure in the original investigation, compare the translational speeds of the two containers.
2. Repeat the procedure using spheres of different radii but with the same mass, such as large glass spheres and small metal spheres of the same mass.
2. How do the translational speeds of similarly shaped but different-size objects compare on a level plane? Design a way to compare these translational speeds. One way is to use different sizes of marbles. Design a way to give the marbles an equal forward force, such as by placing them on a floor in front of a lightweight box. Then snap the backside of the box with your finger.
3.
1. Objects of comparable shapes will roll down an incline at the same translational speed. How do the translational speeds of different shapes compare? Design an experiment to compare the translational speeds of a solid sphere, a disk, and a hoop. One way is to roll all three at the same time and compare their translational speeds. Instead of measuring the translational speeds, you can rate them and compare one to another. For example, the translational speeds of the three objects can be 1, 2, or 3, with 1 being the least amount. Record the information in a Translational Speed Data table like Table 9.1.
2. How do your experimental data for the translational speeds of a solid sphere, a disk, and a hoop compare to the known values for each? Mathematically determine the translational speeds for each of the shapes using the equations in Table 9.2, then compare your calculated values to your experimental data. In each equation, v1 = translational speed, g = gravity (9.8 m/sec2), and h = height of the ramp measured in meters.
4. How does the distribution of mass about the axis of an object rotating down an incline affect its translational speed? Design a way to determine the effect of the location of mass on rotational kinetic energy. One way is to place weights at different distances from the object's axis. For example, use two identical cans with removable lids. Use a thin strip of duct tape to secure five metal washers around the inside rim of the bottom of one can and five washers around the inside rim of its lid. Stack and tape five washers together and use duct tape to secure them in the center of the bottom of the other can. Stack and secure five more washers and attach them to the middle of the inside of that can's lid. Put the lids on both cans. Using the ramp and procedure from the original investigation, compare the translational speeds of the two cans.

### Get the Facts

1. The formula for translational speed of different-shape objects rolling is algebraically determined from the formula for the total mechanical energy. The total mechanical energy of an object at a height above a zero reference is the sum of translational kinetic energy, rotational kinetic energy, and gravitational potential energy. What is the algebraic expression for each of these energies? For information, see a physics text such as John D. Cutnell, Physics: Third Edition (New York: Wiley, 1995), p. 226.
2. The translational speed of a rotating object depends on how much of its kinetic energy is used in turning the object. This is a measure of rotational kinetic energy, which is related to inertia. What is rotational inertia? What is the difference in the rotational inertia of the different shapes investigated in this chapter? For information about the rotational inertia of different shapes, see a physics text; Chapter 10, "Rotational Inertia," in this book; and Robert L. Lehrman, Physics: The Easy Way (Roslyn, N.Y.: Barron's, 1998), pp.101, 132-133.
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