an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the following method. A circular disk of mass 0.53 kg and radius 1.6 cm is glued to the plate, with its center aligned with point O (Figure b). A string is wrapped around the edge of the disk the way a string is wrapped around a top. Then the string is pulled for 5.2 s. As a result, the disk and plate are rotated by a constant force of 0.41 N that is applied by the string tangentially to the edge of the disk. The resulting angular speed is 110 rad/s. What is the rotational inertia of the plate about the axle?
an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the following method. A circular disk of mass 0.53 kg and radius 1.6 cm is glued to the plate, with its center aligned with point O (Figure b). A string is wrapped around the edge of the disk the way a string is wrapped around a top. Then the string is pulled for 5.2 s. As a result, the disk and plate are rotated by a constant force of 0.41 N that is applied by the string tangentially to the edge of the disk. The resulting angular speed is 110 rad/s. What is the rotational inertia of the plate about the axle?
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A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk (the figure (Figure 1)). The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t)=At, where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is 1.90 m/s2 .
(a) Find A. (b) Express the angular acceleration of the disk as a function of time. (c) How much time after the disk has begun to turn does it reach an angular speed of 14.5 rad/s ? (d) Through what angle has the disk turned just as it reaches 14.5 rad/s ? |
