Figure 10.32 shows an apparatus used to measure rotational inertias of various objects, in this case spheres of varying masses M and radii R. The spheres are made of different materials, and some are hollow while others are solid. To perform the experiment, a sphere is mounted to a vertical axle held in a frame with essentially frictionless bearings. A spool of radius b = 2.50 cm is also mounted to the axle, and a string is wrapped around the spool. The string runs horizontally over an essentially frictionless pulley and is tied to a mass m = 77.8 g. As the mass falls, the string imparts a torque to the spool/axle/disk combination, resulting in
FIGURE 10.32 Problem 79
Sphere mass M (g) | 783 | 432 | 286 | 677 | 347 |
Sphere radius R (cm) | 6.25 | 3.86 | 9.34 | 9.42 | 9.12 |
Fall time t (s) | 2.36 | 1.22 | 2.72 | 3.24 | 2.91 |
Sphere mass M (g) | 947 | 189 | 821 | 544 | 417 |
Sphere radius R (cm) | 6.71 | 5.45 | 6.55 | 4.67 | 9.98 |
Fall time t (s) | 2.75 | 1.41 | 2.51 | 1.93 | 3.47 |
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