A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 70 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder. What is her new rotation frequency, in revolutions per second?
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A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 70 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder.
What is her new rotation frequency, in revolutions per second?
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- Four 100 g masses are mounted on a much lighter (assume massless) ring. The ring has a radius of 0.1 m. If the ring is to spin around an axis perpendicular to the plane of the ring and passing through its center, what is the moment of inertia? 0.004 kg m^2 0.04 kg m^2 0.001 kg m^2 0.01 kg m^2 0.002 kg m^2A 45 kg figure skater is spinning on the toes of her skates at 1.3 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg, 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 71 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head. In this latter orientation, she can be modeled as a 45 kg, 20-cm-diameter, 200-cm-tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer in revolutions per second. ► View Available Hint(s) W₂ Submit Provide Feedback ΑΣΦ ? rev/sA figure skater wants to spin faster. With her arms and leg outstretched, she has a moment of inertia1 = 3.6 kgm2 and a spin rate of 2.0 rev/s. If she can squeeze her arms and leg closer to her rotation axis, she can spin at a rate of 24 rev/s. What is her new moment of inertia for the faster spin? O 1.9 kgm2 O 0.30 kgm2 O 7.2 kgm2 O 45 kgm2
- On average, both arms and hands together account for 13% of a person's mass, while the head is 7.0% and the trunk and legs account for 80%. We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 67.0 kg skater is 1.60 m tall, has arms that are each 64.0 cm long (including the hands), and a trunk that can be modeled as being 32.0 cm in diameter. If the skater is initially spinning at 64.0 rpm with her arms outstretched, what will her angular velocity @2 be (in rpm) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble. W2 = rpm Question Source: FreedA uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.50 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles.(a)What is the moment of inertia of the system in kg · m2? (b)If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have? (c)Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2? (d)If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s?A student sits on a freely rotating stool holding two dumbbells, each of mass 3.04 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.08 m from the axis of rotation and the student rotates with an angular speed of 0.757 rad/s. The moment of inertia of the student plus stool is 2.73 kg m² and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.308 m from the rotation axis (Figure b). @₂ Ⓡ (a) Find the new angular speed of the student. rad/s b (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kbefore = Kafter = Need Help? Read It Watch It
- The Bunchberry flower has the fastest moving parts ever observed in a plant. Initially, the stamens are held by the petals in a bent position, storing elastic energy like a coiled spring. When the petals release, the tips of the stamen act like medieval catapults, flipping through a 60° angle in just 0.30 ms.to launch pollen from anther sacs at their ends. The human eye just sees a burst of pollen; only high speed photography reveals the details. We can model the stamen tip as a 1.0 mm long, 10µg rigid rod with a 10µg anther sac at the end. Although oversimplifying, we'll assume a Pollen Pollen Anther sac constant angular acceleration. A. How large is the "straightening torque"? (you may assume the torques created by the gravity 1.0 mm Stamen force are minimal compared to the straightening torque, and can be ignored. B. What is the speed of the anther sac as it releases its pollen? Initial configuration Final configurationA student sits on a rotating stoll holding two 8.0kg objects. When his arms are extended horizontally, the objects are 1.3m from the axis rotation and he rotated with an angular speed of 1.8rad/s. The moment of intertidal of the student plus stoll is 4.5kg•m^2 and is assumed to be constant. if the student pulls in the two objects horizontally to 0.50m from the rotation axis. What is the new angular speed in rad/s of the student? (3 sig fig)In the diagram, disk 1 has a moment of inertia of 4.2 kg · m2 and is rotating in the counterclockwise direction with an angular velocity of 6.5 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular velocity of 8.7 rad/s falls from above onto disk 1. The two then rotate as one in the clockwise direction with an angular velocity of 2.4 rad/s. Determine the moment of inertia, in kg · m2, of disk 2.
- A student sits on a freely rotating stool holding two dumbbells, each of mass 3.07 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.06 m from the axis of rotation and the student rotates with an angular speed of 0.742 rad/s. The moment of inertia of the student plus stool is 2.73 kg· m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.291 m from the rotation axis (Figure b). w; (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kpefore KafterOn average, both arms and hands together account for 13% of a person's mass, while the head is 7.0% and the trunk and legs account for 80%. We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 73.0 kg skater is 1.60 m tall, has arms that are each 74.0 cm long (including the hands), and a trunk that can be modeled as being 37.0 cm in diameter. If the skater is initially spinning at 78.0 rpm with her arms outstretched, what will her angular velocity ω2 be (in rpm) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble. ω2= rpm