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Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.64 m. Disk 1 has a moment of inertia I = 10.7 kg-m². Disk 2 has a moment of inertia I, = 16 kg- m². Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity wi.z = 17.5 rad/s, and disk 2 is initially spinning with a z-component of angular velocity w2,z = -23 rad/s. Disk 1 Disk 2

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.64 m. Disk 1 has a moment of inertia I = 10.7 kg-m². Disk 2 has a moment of inertia I, = 16 kg- m². Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity wi.z = 17.5 rad/s, and disk 2 is initially spinning with a z-component of angular velocity w2,z = -23 rad/s. Disk 1 Disk 2

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I am trying to find the final angular velocity of a cylinder after you throw a ball at it. The knowns are shown in the images that will show the context of the problem. The value I have already solved for is the angular velocity after disk 1 is dropped on disk 2 which is -6.7697 rad/s, the other value is the change in thermal energy created from the collision which is 5258.629 J.

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R= 2.64 m. Disk 1 has a moment of inertia I = 10.7 kg-m2. Disk 2 has a moment of inertia I, = 16 kg: m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity wi,z = 17.5 rad/s, and disk 2 is initially spinning with a z-component of angular velocity w2,z = -23 rad/s. Disk 1 Disk 2
Transcribed Image Text:Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R= 2.64 m. Disk 1 has a moment of inertia I = 10.7 kg-m2. Disk 2 has a moment of inertia I, = 16 kg: m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity wi,z = 17.5 rad/s, and disk 2 is initially spinning with a z-component of angular velocity w2,z = -23 rad/s. Disk 1 Disk 2
You want to speed up the system of rotating disks. To do this, you throw a ball of mass m, at the two disks that are still rotating together with the same speed (just after they collide). You throw the ball at the disks, and the ball follows the following trajectory as viewed from above. The ball of mass m, approaches the disks at an angle 0 with respect to the tangent line to the disk and rebounds at an angle o with respect to the normal. The ball's initial speed is vo, and its final speed is vf. What is the new z-component of the angular velocity of the system of rotating disks (they still rotate together) after the collision with the ball? Use these values for the parameters: Vf = 1.8 m/s vo = 11 m/s 0 = 58° $ = 67.2° ть 3D 1.97 kg R= 2.64 m
Transcribed Image Text:You want to speed up the system of rotating disks. To do this, you throw a ball of mass m, at the two disks that are still rotating together with the same speed (just after they collide). You throw the ball at the disks, and the ball follows the following trajectory as viewed from above. The ball of mass m, approaches the disks at an angle 0 with respect to the tangent line to the disk and rebounds at an angle o with respect to the normal. The ball's initial speed is vo, and its final speed is vf. What is the new z-component of the angular velocity of the system of rotating disks (they still rotate together) after the collision with the ball? Use these values for the parameters: Vf = 1.8 m/s vo = 11 m/s 0 = 58° $ = 67.2° ть 3D 1.97 kg R= 2.64 m
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