Hi there!
a.
We can use the initial conditions to solve for w₀.
It is given that:

We are given that at t = 0, ω = 3.7 rad/sec. We can plug this into the equation:

Now, we can solve for sigma using the other given condition:

b.
The angular acceleration is the DERIVATIVE of the angular velocity function, so:

c.
The angular displacement is the INTEGRAL of the angular velocity function.




Convert this to rev:

d.
We can begin by solving for the time necessary for the angular speed to reach 0 rad/sec.

Evaluate the improper integral:



Convert to rev:

Answer:

Explanation:
The angular speed is given by:

Here v is the linear speed and r is the radius of the circular motion. The height of the tower is equal to the radius of the circular motion of the top of the tower, since is rotating about its base. We need to convert the given linear speed to
:

Now, we calculate the angular speed:

Answer: 47.6 m/s
Explanation: Please see attached for the calculation and formula.