To calculate the final velocities and direction of motion of both objects, we can use the conservation of linear and angular momentum.

Let's assume object 1 has a mass of m1, initial velocity of v1i, and initial angle of motion θ1. Similarly, object 2 has a mass of m2, initial velocity of v2i, and initial angle of motion θ2.

We can calculate the initial linear momentum of each object:

Linear momentum of object 1 (p1i) = m1 * v1i * cos(θ1)
Linear momentum of object 2 (p2i) = m2 * v2i * cos(θ2)

Similarly, we can calculate the initial angular momentum of each object:

Angular momentum of object 1 (L1i) = m1 * v1i * sin(θ1) * r1 ,where r1 is the perpendicular distance from the axis of rotation to object 1.
Angular momentum of object 2 (L2i) = m2 * v2i * sin(θ2) * r2 ,where r2 is the perpendicular distance from the axis of rotation to object 2.

Since the initial angular momentum of both objects is zero (as one of them is at rest), we have:

m1 * v1i * sin(θ1) * r1 = 0
m2 * v2i * sin(θ2) * r2 = 0

Now, let's assume that after the collision, the final velocities of the objects are v1f and v2f, and the angles of motion are θ1' and θ2'.

Using the conservation of linear momentum, we have:

m1 * v1i * cos(θ1) + m2 * v2i * cos(θ2) = m1 * v1f * cos(θ1') + m2 * v2f * cos(θ2')

Using the conservation of angular momentum, we have:

m1 * v1i * sin(θ1) * r1 + m2 * v2i * sin(θ2) * r2 = m1 * v1f * sin(θ1') * r1 + m2 * v2f * sin(θ2') * r2

Solving these two equations simultaneously will give us the final velocities v1f and v2f, as well as the angles of motion θ1' and θ2'.

Please note that the values of r1 and r2 depend on the specific setup of the collision and the axis of rotation.

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