A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical axis through its center. A 63.3 kg person stands on the platform at a distance of 1.19 m from the center, and a 26.9 kg dog sits on the platform near the person 1.31 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.
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- A cockroach of mass m lies on the rim of a uniform disk of mass 8.00m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.320 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then iş the angular velocity of the cockroach-disk system? rad/s (b) What is the ratio K/Ko of the new kinetic energy of the system to its initial kinetic energy? (c) What accounts for the change in the kinetic energy? (Select all that apply.) O cockroach does negative work on the disk O gravity O centripetal force O friction O centrifugal force O cockroach does positive work on the diskA weather vane initially at rest has a moment of inertia of 0.123 kg · m2 about its axis of rotation. A 57.0 g piece of clay is thrown at the vane and sticks to it at a point 24.5 cm from the axis. The initial velocity of the clay is 23.0 m/s, directed perpendicular to the vane. Find the angular velocity of the weather vane just after it is struck. please solveIn the figure, a 5.25 g bullet is fired into a 0.547 kg block attached to the end of a 0.718 m nonuniform rod of mass 0.117 kg. The block- rod-bullet system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about A is 0.0577 kg-m2. Treat the block as a particle. (a) What then is the rotational inertia of the block-rod-bullet system about point A? (b) If the angular speed of the system about A just after impact is 4.31 rad/s, what is the bullet's speed just before impact? Rod Block Bullet (a) Number Units (b) Number i Units
- A weather vane initially at rest has a moment of inertia of 0.104 kg · m2 about its axis of rotation. A 68.0 g piece of clay is thrown at the vane and sticks to it at a point 14.0 cm from the axis. The initial velocity of the clay is 27.5 m/s, directed perpendicular to the vane. Find the angular velocity of the weather vane just after it is struck.A skater goes for a jump with turns. When she extends her arms, her moment of inertia about an axis through his body is 1.750 kg*m2. She initially pins at 0.650 rev/s and launches herself into the air and remained there for about 1.570 seconds while spinning at a constant angular speed. Assuming that her moment of inertia about an axis through his body has a value of 0.62 kg*m2, determine how many revolutions can she execute.Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 110 kg-m2. When one person is standing at a distance of 1.71 m from the center, the carousel has an angular velocity of 0.644 rad/s. However, as this person moves inward to a point located 0.641 m from the center, the angular velocity increases to 0.832 rad/s. What is the person's mass? | | Number i Units
- John McClane, desperately trying to escape the bad guys in an upper floor of a skyscraper, grabs a fire hose and crashes out a window. He falls toward the ground, dragging the hose with him. The hose is wound around a cylinder that has a moment of inertia equal to 5 kg m2, and the hose unspools from the cylinder as McClane falls. Assuming that the hose is pulled from the cylinder at an angle that is perpendicular to the cylinder's radius, what is McClane's acceleration? Let McClane's mass be 75 kg and the radius of the cylinder be 0.5 m. Neglect friction and air resistance. Hose Wall Spool McClaneYou stand on a frictional platform that is rotating at 1.6 rev/s. Your arms are outstretched, and you hold a heavy weight in each hand. The moment of inertia of you, the extended weights, and the platform is 7.9 kg · m2. When you pull the weights in toward your body, the moment of inertia decreases to 3.7 kg · m2. (a) What is the resulting angular speed of the platform?(b) What is the change in kinetic energy of the system?(c) Where did this increase in energy come from? (Select all that apply.) -your internal energy -gravity -kinetic energy of the platform -mass of the weights -air resistanceConceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg-m². When one person is standing on the carousel at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.600 rad/s. However, as this person moves inward to a point located 0.917 m from the center, the angular velocity increases to 0.800 rad/s. What is the porcon's marr?
- A 139-kg platform-oriented horizontally consists of a uniform disk of radius 1.85 m and can rotate about the vertical axis through its center. A 63.3-kg person stands on the platform at a distance of 1.17 m from the center and a 27.5-kg dog sits on the platform near the person, 1.39 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.A girl of mass 20.3 kg stands on the rim of a frictionless merry-go-round of radius 1.29 m and rotational inertia 455 kg-m2 that is not moving. She throws a rock of mass 584 g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 5.22 m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl? (a) Number i Units (b) Number i UnitsConsider the setup shown below. The blocks have masses 3.6 kg and 24 kg. The pulley has mass 7.4 kg, and is a uniform disc with radius 0.23 m. Assume the pulley to be frictionless, but the coefficient of friction between the block and the surface is 0.36. What is the acceleration of the blocks? Assume the 24 kg mass is descending with acceleration a. The moment of inertia of the disk is 1/2MR2 and the acceleration of gravity is 9.8 m/s2.