The blades of a ceiling fan have a radius of 0.399 m and are rotating about a fixed axis with an angular velocity of +1.65 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 2.08 rad/s2. After 0.520 s have elapsed since the switch was reset, what are the following?

The following what?

To find the following quantities, we need to use the equations of rotational motion. The given information includes:

- Radius of the ceiling fan blades (r) = 0.399 m
- Initial angular velocity (ω₀) = +1.65 rad/s
- Angular acceleration (α) = 2.08 rad/s²
- Time (t) = 0.520 s

We need to find the following quantities:
- Final angular velocity (ω)
- Total angular displacement (θ)
- Tangential velocity (v)

First, let's find the final angular velocity (ω):
Using the equation of rotational motion,
ω = ω₀ + αt
ω = 1.65 rad/s + (2.08 rad/s²)(0.520 s)
ω = 2.706 rad/s (rounded to three decimal places)

Next, let's find the total angular displacement (θ):
Using the equation of rotational motion,
θ = ω₀t + 0.5αt²
θ = (1.65 rad/s)(0.520 s) + 0.5(2.08 rad/s²)(0.520 s)²
θ = 0.858 rad (rounded to three decimal places)

Finally, let's find the tangential velocity (v):
The tangential velocity is related to the angular velocity by the equation:
v = rω
v = (0.399 m)(2.706 rad/s)
v = 1.082 m/s (rounded to three decimal places)

Therefore, the following quantities are:
- Final angular velocity (ω) = 2.706 rad/s
- Total angular displacement (θ) = 0.858 rad
- Tangential velocity (v) = 1.082 m/s