A 49.7-cm diameter disk rotates with a constant angular acceleration of 2.7 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.

There is no question here. Just a bunch of numbers.

To find the angle through which the disk rotates, we need to calculate the angular displacement. Angular displacement is given by the equation:

θ = θ₀ + ω₀t + (1/2)αt²

Where:
θ is the angular displacement,
θ₀ is the initial angular position (in radians),
ω₀ is the initial angular velocity (in radians per second),
α is the angular acceleration (in radians per second squared),
t is the time (in seconds).

In this case, the disk starts from rest, so the initial angular velocity (ω₀) is 0, and the initial angular position (θ₀) is the angle (in radians) between the line drawn from the center of the disk to point P on the rim and the positive x-axis, which is given as 57.3°.

First, we need to convert the angle to radians by multiplying it by (π/180):

θ₀ = (57.3°) x (π/180) = 1.00029 radians (approximately)

Next, substitute the given values into the equation:

θ = θ₀ + ω₀t + (1/2)αt²
θ = 1.00029 + 0 + (1/2)(2.7)(t²)
θ = 1.00029 + 1.35t²

We can solve for t by rearranging the equation:

t² = (θ - θ₀) / 1.35
t² = (θ - 1.00029) / 1.35
t = √((θ - 1.00029) / 1.35)

Now, we can substitute the given angle, θ, and calculate t:

t = √((57.3° x (π/180) - 1.00029) / 1.35)
t = √((1 - 1.00029) / 1.35)
t = √( -0.00029 / 1.35)
t = √( -0.0000002148 )
t = 0

Since the result is t=0, it means that the line drawn from the center of the disk to point P on the rim makes an angle of 57.3° with the positive x-axis at t=0. Therefore, the disk has not yet rotated.