You have a pulley 13.9 cm in diameter and with a mass of 1.7 kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is it concentrated toward the center or the rim? To find out, you hang the pulley on a hook, wrap a string around it several times, and suspend your 1.1 kg physics book 1.3 m above the floor. With your stopwatch, you can find that it takes 0.66 s for your book to hit the floor.

To determine whether the mass of the pulley is evenly distributed or concentrated towards the center or rim, we can use the principle of torque.

First, let's break down the given information:
- Diameter of the pulley = 13.9 cm
- Mass of the pulley = 1.7 kg
- Mass of the physics book = 1.1 kg
- Distance from the pulley's center to the floor = 1.3 m
- Time taken for the book to hit the floor = 0.66 s

To solve this problem, we will make use of the equation of motion related to rotational dynamics:

τ = Iα

Where:
τ = Torque
I = Moment of inertia
α = Angular acceleration

The torque acting on the system is the weight of the book acting tangentially to the pulley. It can be calculated as follows:
τ = mgR

Where:
m = Mass of the book
g = Acceleration due to gravity
R = Radius of the pulley (half of its diameter)

The moment of inertia for a pulley is given by:
I = (1/2) MR^2

Where:
M = Mass of the pulley
R = Radius of the pulley

We can find the angular acceleration using the equation:
α = Δθ/Δt = 2πN/t
where:
Δθ = change in angular displacement (2π radians)
N = number of rotations
t = time taken for N rotations

In this case, the angular acceleration is constant throughout the book's descent.

Now, let's calculate the torque acting on the system:
τ = mgR = (1.1 kg) * (9.8 m/s^2) * (0.139 m/2) = 0.722 kg * m^2/s^2

Next, we can calculate the number of rotations the pulley makes during the time taken for the book to hit the floor:
N = (Δθ * t) / (2π) = (2π rad * 0.66 s) / (2π) = 0.66 rotations

With the number of rotations known, we can calculate the angular acceleration:
α = (2π * N) / t = (2π * 0.66) / 0.66 = 2π rad/s^2

Now we have all the information required to find the moment of inertia of the pulley:
I = (1/2) * M * R^2 = (1/2) * 1.7 kg * (0.139 m/2)^2 = 0.008 kg * m^2

Finally, rearranging the torque equation τ = Iα, we can determine if the mass is evenly distributed or not:
0.722 kg * m^2/s^2 = 0.008 kg * m^2 * α

Therefore, the angular acceleration α is approximately 90.3 rad/s^2. Since the angular acceleration is non-zero, this suggests that the mass of the pulley is not evenly distributed and is concentrated towards either the center or the rim.