Answer:
Part(a): The final angular velocity is 
Part(b): The ratio of the rotational energies is
,showing the the energy of th system will decrease.
Explanation:
Part(a):
If '
' be the moment of inertia of an object and '
' be its angular velocity then the angular momentum '
' of the object can be written as

If '
' and '
' be the moment of inertia of the two cylinders and '
' and '
' be the initial angular velocity of the cylinders and '
' and '
' be their respective final angular velocity, then from conservation of angular momentum,

Given,
. From the above expression

Part(b):
Initial kinetic energy
and Final kinetic energy

Substituting the value of
,

The above expression shows that the ebergy of the system will decrease.
Answer:
d. 8 feet
Explanation:
(height)^2 = (10)^2 - (6)^2
= 100 - 36
height = √64
= 8 feet
If we have the angle and magnitude of a vector A we can find its Cartesian components using the following formula

Where | A | is the magnitude of the vector and
is the angle that it forms with the x axis in the opposite direction to the hands of the clock.
In this problem we know the value of Ax and Ay and we need the angle
.
Vector A is in the 4th quadrant
So:

So:

So:

= -47.28 ° +360° = 313 °
= 313 °
Option 4.