Answer:
The angular velocity at the beginning of the interval is
.
Explanation:
Given that,
Angular acceleration 
Angular displacement 
Angular velocity 
We need to calculate the angular velocity at the beginning
Using formula of angular velocity


Where,
= angular acceleration
= angular velocity
Put the value into the formula



Hence, The angular velocity at the beginning of the interval is
.
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Relative to the positive horizontal axis, rope 1 makes an angle of 90 + 20 = 110 degrees, while rope 2 makes an angle of 90 - 30 = 60 degrees.
By Newton's second law,
- the net horizontal force acting on the beam is

where
are the magnitudes of the tensions in ropes 1 and 2, respectively;
- the net vertical force acting on the beam is

where
and
.
Eliminating
, we have





Solve for
.



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