*41 In Fig. 10-37, two particles, cach with mass m=0.85 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.6 cm and mass M= 1.2 kg. The combination rotates around the rotation axis with the angular speed o = 0.30 rad/s. Measured about O, what are the combination's (a) rotational inertia and (b) kinetic energy? M Rotation axis
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- In the figure below, the disk, of mass 440 g and radius 3.5 cm, is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.3 cm, is initially not rotating. It drops freely down onto the lower dis, and frictional forces bring the two disk to a common rotational speed. Find (a) that common speed and (b) the fraction of the initial kinetic energy lost to friction.A playground merry-go-round with an axis at the center (radius R = 1.5 m and rotational inertia | = 1.33 x 103 kgm²) is initially rotating at angular velocity wo = 1.1 rad/s (counter-clockwise). A girl of mass m = 39 kg is running at speed vo = 3.3 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the point labeled with the green "x" (she is indicated by the purple circle in the figure). What is the angular momentum of the girl relative to the rotation axis of the merry-go-round? Your answer should be in kgm²/s, but enter only the numerical part in the box. R WoGiven a mass of 380 grams, and a rotational speed 180 rpm, calculate the maximum rotational kinetic energy for the following three shapes: a disk, a sphere and a thin rod. Both, the disk and the sphere have a radius of 20 cm, and the length of the thin rod is 40 cm. If the same mass is shaped as a hoop with a radius of 20 cm, would be the rotational kinetic energy greater, or smaller than the kinetic energies calculated for the other 3 shapes? Check your prediction - calculate the rotational kinetic energy for that shape, and compare your results. Was your answer consistent with your expectations?
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- In Fig. 10-34, two particles, each with mass m = 0.85 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d= 5.6 cm and mass M = 1.2 kg. The combination rotates around the rotation axis with the angular speed = 0.30 rad/s. Measured about O, what are the combination's (a) rotational inertia and (b) kinetic energy? (1) M Rotation axis 2M m 4 10) The rigid body consists of three particles connected by massless rods. It is to be rotated about an axis perpendicular to its plane through point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? M 4 m 2MA disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 6.60 rev/s; 45.0 revolutions later, its angular speed is 24.0 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 45.0 revolutions, (c) the time required to reach the 6.60 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 6.60 rev/s angular speed. (a) Number Unit (b) Number i Unit (c) Number i Unit (d) Number Unit