Determine equivalent inertia and equivalent stiffness of the system shown in Figure. Mass of the bar is M. Use rotation of the bar (0) as the generalized coordinate. L L/4 2m k₁ m 2k
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vibrations - solve and show all steps
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- Match the most appropriate form of the equation for the moment of inertia to the image shown. All objects are rotating about point O. Note: ris distance, m is a mass, k is a radius of gyration and d is a distance from the mass moment of inertia IG about the center of mass A. D. O M X Mass element Z Rotation axis X A.1=1+md² G B. = SM √² r²dm C.I=mk²_ D.1= Σm,r?Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt. mass1=10kg Jo=20kg-m2 mass2=15kg, a is half of b. The rocker is 30 centimeters long. (kg-m2)5. Calculate the moments of inertia I1, I2, and I3 for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the origin at the apex of the cone, and calculate the elements of the inertia tensor. Then make a transformation such that the center of mass of the cone becomes the origin, and find the principal moments of inertia.
- The figure below shows an assembly consists of a thin rod ( mass 1.4 kg and length 1 m) and two spheres ( top and bottom) with m;=0.2 kg, R1=0.1 m and m2=0.3 kg, R2=0.3 m. If the assembly is free to rotate around point O, the moment of inertia of the assembly in kgm2 is 2 ( Icom, rod = 1 ML2 , Icom,sphere=mR2) 12 R1 Sphere 1 Rod L/2 R2 Sphere 2Two balls of mass ma and m, are connected by a massless rod of length L. The two vertical dashed lines in the figure, below, represent two different axes of rotation (axes a and b). These axes are parallel to each other and perpendicular to the rod. If the ratio between the two moments of inertia, as measured relative to each axis, is 4 = 3. Ib a. Find the ratio of the masses (ma/mp). b. Find the distance from ball a to the system's center of mass. Axis a Axis b L- ma Two balls connected by a massless rod of length L rotate around the two axes shown.Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt mass1=5kg Jo=20kg-m2 mass2=2kg, a is half of b. The rocker is 3 meters long. (kg-m2) *
- Please show a detailed solution for the computation of moment of inertia.Hello, please solve this question. Thank you very muchwheel with a mass of 20 kg and a radius of inertia of 300mm, moves under the influence of a torque of 100Nm. Find the angular acceleration of the wheel, the linear acceleration of its center O, the wheel pressure n the ground N, and the mass moment of inertia J. Give the result to 2 decimal places.
- 4. Determine the moment of inertia and the radius of Gyration about the axis of rotation for the wheel shown in the figure below. The density of the material can be taken as 7000kg/m³ 100mm 25 mm 50 mm Dia 250mm 300mm Dia DiaThere is a pirate ship in the harbor which features a large, cast iron wheel that is used to steer the ship. As shown in the figure above, this wheel features spokes with a length of R = 0.83 meters, configured as shown. Star symbols indicate specific points on the wheel (labelled A, B, C, D, and E). The moment of inertia of this wheel is I = 12.2 kg⋅m2.The wheel spins around a gear mechanism attached at its center. The gear mechanism has sufficient resistance (due to friction and other factors) that anyone trying to turn the wheel feels a counter-torque of τres = 10 N⋅m. After the wheel begins moving, a constant resisting torque of τres = 10 N⋅m is still felt. Someone applies a a tourque of 33.7N*mvto the wheel for five seconds, if the wheel starts at rest what is it anuglar momentum after five seconds? If the wheel is now spinning at 1 rad/sec what is the magnitude of the tourque to keep it spinning? What is the total kinetic magnitude of the wheel ( the mass is 4kg)For the body shown. If point P3 is the center of mass for rod part P1-P2, and point P4 is the center of mass for rod part P3-P5, and P6 is the center of mass of the disk part. Find the mass moment of inertia around axis perpendicular to the page and passes through point P5. Given; L = 1 m, mass density of rod parts = 5 kg / m, mass density of disk = 12 Kg / m?