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 = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 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 = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. here is what I have found so far: The z component of their common angular velcoity is 8.837 rad/s The thermal energy created by disk one falling on disk 2 is 2145.5 J vf = 2.2 m/s v0 = 14 m/s θ = 65.7∘ ϕ = 75.2∘ mb = 1.62 kg R = 2.58 m ωnew,z= 9.83 rad/s HERE IS WHAT I AM HAVING TROUBLE WITH: Starting with ωnew,z you now want to immediately slow the system down, so you decide to throw a mud ball ( mmud = 2 kg ) at the system of rotating disks. The trajectory from above looks like this: The mud is moving with initial speed vmud = 26 m/s and sticks to the rim of the disk upon impact. The distance d = 1 m. Find the common final z-component of the angular velocity of the two disks and the mud. As a reminder, positive z-components correspond to counterclockwise rotation as viewed from above.
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 = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 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
here is what I have found so far:
The z component of their common angular velcoity is 8.837 rad/s
The thermal energy created by disk one falling on disk 2 is 2145.5 J
vf = 2.2 m/s
v0 = 14 m/s
θ = 65.7∘
ϕ = 75.2∘
mb = 1.62 kg
R = 2.58 m
ωnew,z= 9.83 rad/s
HERE IS WHAT I AM HAVING TROUBLE WITH:
Starting with ωnew,z you now want to immediately slow the system down, so you decide to throw a mud ball ( mmud = 2 kg ) at the system of rotating disks. The trajectory from above looks like this:
The mud is moving with initial speed vmud = 26 m/s and sticks to the rim of the disk upon impact. The distance d = 1 m. Find the common final z-component of the angular velocity of the two disks and the mud. As a reminder, positive z-components correspond to counterclockwise rotation as viewed from above.
the answer I have been getting is 7.025 rad/s which is wrong. Where am I going wrong?
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