You want to speed up the system of rotating disks. To do this, you throw a ball of mass mb 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 mb approaches the disks at an angle θ with respect to the tangent line to the disk and rebounds at an angle ϕ with respect to the normal. The ball's initial speed is v_0, and its final speed is v_f.
- 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 (associated with image 1):
v_f=2.13 m/s
v_0=14.2 m/s
θ=63.2∘
ϕ=68.7∘
m_b=1.59 kg
R=2.68 m
*Initial scenario if it helps*
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=2.68 m. Disk 1 has a moment of inertia I1=11.1 kg⋅m2. Disk 2 has a moment of inertia I2=16.6 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 ω1,z=10.3 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z=−15.5 rad/s.
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