A disk has a moment of inertia of 2.50 x 10°2 kg-m² and spins on a frictionless axis through its center at an initial angular speed of 22.2 rad/s. A ring, initially not rotating, of mass 0.250 kg and radius 0.200 m, is dropped vertically onto the disk and sticks so that the combination rotates about a common axis, through their centers. What is the new angular speed of the system? Note: I¡ing: MR². %3D
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- A solid disk rotates in the horizontal plane at an angular velocity of 0.042 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.089 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance 0.29 m from the axis. The sand in the ring has a mass of 0.42 kg. After all the sand is in place, what is the angular velocity of the disk?The figure shows three uniform solid disks, each of mass 7.8 kg and radius 0.3 m rotating independently around a common axle. Two of the disks rotate in one direction at 5.3 rad/s while the other rotates in the opposite direction at 3.6 rad/s. Calculate the magnitude of the system's angular momentum about a point in the middle of the center disk. L= kg m²/s - Report your numerical answer below, assuming three significant figures. Remember to include a "-" when necessary.A disk of mass M is spinning freely at 9.27 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. HINT (a) What is the angular speed of the new system (in rad/s)? rad/s (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s). rad/s
- A thin rod has a length of 0.537 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.778 rad/s and a moment of inertia of 1.10 x 10³ kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?A 70 kg disk is spinning about a vertical axis of rotation with a radius of 1.2 m and a rotational inertia of 0.45 mr2 and it has an initial angular velocity of 10 rad/s. An unknown mass falls onto the disk 0.8 m away from the axis of rotation. After the collision, the disk is now spinning at 6 rad/s. The rotational inertia of the mass is mr2. Calculate the unknown mass that falls on the disk.A wheel rotates clockwise about its central axis with an angular momentum of 600Kg.m 2 /s.At time t= 0, a torque of magnitude 50N.m is applied to the wheel to reverse the rotation. If the same torque is maintained, at what time will the angular momentum be counter-clockwise of 600Kg.m 2 /s?
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