The figure shows an overhead view of a uniform 2.00-kg plastic rod of length 1.20 m on a very slick table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 36.0 g slides without friction toward the opposite end of the rod with an initial speed of 23.0 m/s and in the direction shown. The disk strikes the rod and sticks to it. After the collision, the rod (with the disk stuck to its end) rotates about the pivot point. For the question below, treat the disk as if it were a point mass.

(a) What is the angular velocity of the two after the collision?
rad/s

(b) What is the kinetic energy before and after the collision?
KEi
= J
KEf
= J

To find the solutions to parts (a) and (b) of the question, we need to apply the principles of conservation of linear momentum and conservation of mechanical energy.

For part (a), we need to find the angular velocity of the rod with the disk after the collision. The conservation of linear momentum states that the total linear momentum before the collision is equal to the total linear momentum after the collision.

The initial linear momentum of the disk is given by:
p_initial = m_disk * v_initial
where m_disk is the mass of the disk and v_initial is its initial velocity.

The final linear momentum of the rod with the attached disk is given by:
p_final = (m_rod + m_disk) * v_final
where m_rod is the mass of the rod.

Since there is no external torque acting on the system, angular momentum is conserved as well. The initial angular momentum is zero because the rod is initially at rest and the disk is moving only in a straight line.

After the collision, the angular momentum of the system is given by:
L_final = I * ω
where I is the moment of inertia of the system, and ω is the angular velocity.

Since the system consists of a rod and a disk attached to it, the moment of inertia can be calculated as the sum of the individual moment of inertia of the rod and the disk:
I = I_rod + I_disk
where I_rod = (1/3) * m_rod * L^2 and I_disk = m_disk * R^2, with R being the distance from the pivot point to the disk.

Now we can set up the equations:
p_initial = p_final (conservation of linear momentum)
0 = I * ω (conservation of angular momentum)

Solving for the unknowns:
1. Use the conservation of linear momentum equation to find the final velocity of the system (v_final).
2. Use the definition of angular momentum to find the angular velocity (ω) in terms of the final velocity and the moment of inertia of the system.

For part (b), we need to find the kinetic energy before and after the collision. The kinetic energy before the collision is simply the kinetic energy of the disk given by:
KE_initial = (1/2) * m_disk * (v_initial)^2

The kinetic energy after the collision is the sum of the kinetic energy of the rod (which is rotating) and the kinetic energy of the disk attached to it:
KE_final = (1/2) * I * (ω)^2 + (1/2) * m_disk * (v_final)^2

Substituting the expressions for I and ω obtained from part (a), we can find the respective kinetic energies.

Please provide the numerical values for the masses, lengths, and initial velocity in order to calculate the final values.