A student sits on a rotating stool holding two 2.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg-m2 and is assumed to be constant. The student then pulls the objects horizontally to 0.40 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student system before and after the objects are pulled in. before after
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- A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.947 rad/s. You, with a mass of 75.1 kg, walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 20.3 kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 18.9 kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 92.7 kg and radius 1.95 m. Calculate the total angular momentum of the system. total angular momentum: kg · m?/sYou 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 resistanceA cord is wrapped around the rim of a wheel 0.300 m in radius, and a steady pull of 38.5 NN is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.35 kg⋅m2 Compute the angular acceleration of the wheel.
- A cord is wrapped around the rim of a wheel 0.225 m in radius, and a steady pull of 41.5 N is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.50 kg m² 世 ProvConceptual 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 student sits on a rotating stool holding two 3.20-kg objects. When his arms are extended horizontally, the objects are 1.00 m from the axis of rotation and he rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg • m and is assumed to be constant. The student then pulls in the objects horizontally to 0.490 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the system (student/stool/objects) before and after the objects are pulled in. before J after
- A space station shaped like a giant wheel has a radius 103 m and a moment of inertia of 4.97 x 108 kg-m². A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1 g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg. m/s²A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg-m? and is assumed to be constant. The student then pulls the objects horizontally to 0.20 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student system before and after the objects are pulled in. before afterA circular disk with a radius of 0.5 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.69 kg. The moment of inertia of a disc is I MR² = F₁ = 2.6 N applied at the outer edge of the disc. F₂ = 4 N applied at a distance of 0.26 from the center of the disc. What is the angular acceleration of the disc?