Seven identical circular planar discs, each of mass M and radius R are welded symmetrically as shown in the figure. The moment of inertia of the arrangement about an axis normal to the plane and passing through the point P is 181 2 55 MR² 19 MR2 (o), MR 2 2 (a) MR² (b) MR² (d) MR² 73 2
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- A net torque is acting on the two particles shown in the figure for two seconds. Given the information below: (a) Calculate the magnitude and direction of the net angular momentum of particles A and B about the origin point O. (b) Then find the net torque acting this system about point O. mĄ = 6.2 kg тв 3D 3.1 kg VA = 1.2 m/s %3D Vв 3D 2.6 т/s ri = 1.5 m r2 = = 2.7 m VB AA space probe in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope is I, = 24.5 kg • m about the axis of the gyroscope, and the moment of inertia of the rest of the space probe is I, = 5.00 x 105 kg · m2 about the same axis. Initially both the space probe and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 150 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the space probe's orientation by 26.0°?The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia l?
- While placing a compact disc into a CD player, you notice a small chip on its edge. You attempt to play the CD anyway by placing the CD into the player's deck with the chip at ?0=15.2∘θ0=15.2∘ as measured from the +?+x‑axis. The CD begins to rotate with angular acceleration ?=2.31 rad/s2.α=2.31 rad/s2. If the CD has been spinning for ?=3.51 st=3.51 s and the disc has a radius of ?=6.00 cm,r=6.00 cm, what are the ?–?x–y coordinates of the chip after this time, assuming the center of the disc is located at (0.00,0.00)The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.872 m, and rotating with an angular speed of 101 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.268 rad. From these data, determine the speed of the bullet. Number IN Bullet Units MotorA hoop, a solid cylinder, a solid sphere, and a thin, spherical shell each have the same mass of 4.70 kg and the same radius of 0.263 m. (a) What is the moment of inertia (in kg · m2) for each object as it rotates about its axis? hoop kg · m2 solid cylinder kg m2 solid sphere kg · m2 thin, spherical shell kg · m2 (b) Each object is rolled down the same ramp, each starting from rest at the same initial height. Each rolls without slipping. Rank the translational speed at the bottom of the ramp for each object from highest to lowest. O solid cylinder > thin spherical shell > solid sphere > hoop O solid sphere > solid cylinder > thin spherical shell > hoop hoop > solid cylinder > solid sphere > thin spherical shell O thin spherical shell > solid sphere > solid cylinder > hoop (c) As in part (b), each object is rolled down the same ramp, each starting from rest at the same initial height. Each rolls without slipping. Rank the rotational kinetic energy at the bottom of the ramp for each…