A non-uniform rod of length and mass Mis pivoted about one end. The moment of inertia of this rod about its pivoted end is 1ML2/4. Attached to the rod is a mass 3M at its midpoint and at the end opposite the pivot is another mass M. What is the moment of inertia of this configuration about the pivot? 3ML2 2ML2 4ML2 5ML2
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- Suppose that there are two solid steel spheres. The second sphere has a radius twice as large as the radius of the first sphere. What is the ratio of the moments of inertia of the spheres, I2:I1? 8 4 32 2 16Two barbells are sitting on the floor at the RWC. Both consist of a 10 kg bar with length 1.5 m, and two 25 kg plates. On the first barbell, both plates are located at the same end of the bar, while on the second barbell they are located at opposite ends. Which barbell has a larger moment of inertia? A The barbell with both weights at the same end B The barbell with the two weights located at opposite ends C Both have the same moment of inertia D Neither bar bell has a moment of inertia, since they aren't rotating E There isn't enough information to tell, since the moment of inertia depends on the choice of rotational axisThe three 'point' masses are as shown in the figure. m, = 2.0 kg at (x, y) =(0,0), m₂ = 3.0 kg at (4,3), and m3 = 4.0 kg at (8,0), respectively. What is the moment of inertia of the masses about the y axis? +y=3 m x=4 m
- Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius 2R) are connected by a thin, uniform rod of length 3R and mass M as shown in the Figure below. Find the moment of inertia about the axis through the center of the rod. 5.91 MR2 15.1 MR2 10.3 MR2 21.3 MR2Calculate the moment of inertia of the object shown about an axis coming perpendicularly out of the paper, and passing through the leftmost mass. Give: M = 9 kg, L = 2 m, and the connecting rods are mass-less. Treat the masses as point masses.The axis of rotation of a thin plate is located at the left side, as shown in the figure. Calculate the moment of inertia I if the plate has a length L of 7.00 cm, a width W of 5.00 cm, and a uniform mass density of 3.25 g/cm2.
- Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared. b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities. c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.Everyone's favorite flying sport disk can be approximated as the combination of a thin outer hoop and a uniform disk, both of diameter Da = 0.273 m. The mass of the hoop part is mh = : 0.120 kg and the mass of the disk part is md = 0.050 kg. Imagine making a boomerang that has the same total moment of inertia around its center as the sport disk. The boomerang is to be constructed in the shape of an "X," which can be approximated as two thin, uniform rods joined at their midpoints. If the total mass of the boomerang is to be m₁ = 0.235 kg, what must be the length Lы of the boomerang? | I Lb = = Cross-sectional view mA small, heavy mass is at the end of a thin rod with negligible mass. If the mass is 6.4 kg, the rod is 0.56 meters long, and the rod is pivoting around the end opposite the mass, what is the moment of inertia of the rod and mass?
- The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Figure 1). When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg. When outstretched, they span 1.6 m ; when wrapped, they form a thin-walled hollow cylinder of radius 26 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.4 kg⋅m2. If his original angular speed is 0.30 rev/s, what is his final angular speed?Three point objects with masses ?1=2.6 kg, ?2=4.0 kg,and ?3=0.90 kg are arranged in the configuration shown in the figure. The distance to mass ?1 is ?1=25 cm and the distance to mass ?3 is ?3=41 cm. The distances are measured from the axis ?. What is the combined moment of inertia ? for the three point objects about the axis ? ?of Sides a and b has a mass M. Four point-like balls, each of rnass m = each corner of the plate as indicated in the figure. What is the moment of inertia of this object if the axis of M are glued to rotation is through the end of one sidt, like a door, as indicated in the figure by the blue fine? (A) Isoor=M (a² + b²) (B) Isoor= M(a² + b) (C) Idoor M(a² + b*) (D) Isoor = }M(a²+8) (F) Isoor = Ma² %3D (G) Isoor Ma? %3D (H) Idor Ma² A rectangular plate with four umall point-like balls glued to each corner. The blue line represents the axis of rotation