n object is formed by attaching a uniform, thin rod with a mass of mr = 6.86 kg and length L = 5.76 m to a uniform sphere with mass ms = 34.3 kg and radius R = 1.44 m. Note ms = 5mr and L = 4R. What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a
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- A 129 kg129 kg horizontal platform is a uniform disk of radius 1.89 m1.89 m and can rotate about the vertical axis through its center. A 63.9 kg63.9 kg person stands on the platform at a distance of 1.17 m1.17 m from the center, and a 28.7 kg28.7 kg dog sits on the platform near the person 1.43 m1.43 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 tennis racket has a mass of 0.4 kg. The radius of gyration of the racket about its longitudinal axis is 7.5 cm, and its radius of gyration about its swing axis is 0.635m. What is the moment of inertia of this racket about its swing axis.A "Lazy Susan" food tray is being rotated by a person in quest of sustenance. Suppose the person exerts a 2.60 N force perpendicular to the Lazy Susan's 0.260 m radius for 0.240 s. (a) What is the final angular momentum of the Lazy Susan, in kg · m²/s, if it starts from rest, assuming friction is negligible? 0.16224 kg. m²/s (b) What is the final angular velocity of the Lazy Susan in rev/s, given that its mass is 2.80 kg and assuming its moment of inertia is that of a disk? X The Lazy Susan is in the form of a solid disk. rev/s
- Two spheres each with a radius of 5.0 cm and mass of 0.50 kg are free to slide along a thin rod with a of length 50 cm and a mass of 2 kg rotating counterclockwise about the center of the rod. Initially, the moment of inertia of the system is 0.255 kg*m². The beads slide to the end of the rod, which changes the moment of inertia to 0.377 kg*m. The tangential speed of either of the spheres after the beads have slid to the end is 20 m/s. What was the initial angular velocity? intial finalFour particles at the corners of a square with a side length L=5.00m are connected by massless rods. The particle masses are m1= m4=6.00kg and m2= m3 = 14.0 kg. Pairs of particles with equal masses are located at opposite corners of the square. Find the moment of inertia of the system about the z-axis that passes through a corner of the square where the particle has a mass of m=14.00kg.A uniform disk of mass 7 kg and radius 0.2 m is free to rotated about an axis perpendicular to its center. A constant force of size 146 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 169 full rotations. What is the angular momentum of the disk after those rotations are complete, in kg m2/s? It could be useful to you to know that the rotational inertia of a uniform disk is 1/2 M R2. (Please answer to the fourth decimal place - i.e 14.3225)
- A small block of mass m2 hangs from a massless rope wrapped around the inner cylinder of a pulley with inner radius of R2. The moment of inertia of the entire pulley is I = 4m2(R2)?. Another block m1=m2 is connected to the outer cylinder of the pulley via a horizontal massless rope wrapped around the outer cylinder of the pulley with radius R1=2R2. The coefficient of kinetic friction between the block and the horizontal surface is µk = (i.e. the frictional force is f = mig). When m2 is released from rest, what is the angular acceleration a of the block and pulley system? т, m, T, Pick the correct answer 3 g 16 R 最 3Consider the system shown below where four point masses are connected to each other by massless rods. Two of the masses are m = 7 kg and the other two have the masses of M = 3 kg. If a = 1.2 m, b = 0.7 m and the system rotates about y – axis, determine the moment of inertia of the system. Express your answer in units of kg · m? using one decimal place. a a M M m Answer:A 45 kg figure skater is spinning on the toes of her skates at 1.5 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. In this latter orientation, she can be modeled as a 45 kg, 20-cm-diameter, 200-cm-tall cylinder.What is her new rotation frequency, in revolutions per second?Express your answer in revolutions per second.