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To solve this problem, let's break down the information provided and apply the necessary formulas for radial (centripetal) acceleration.

### Given Information:
1. **Radius** of the disk, \( r = 0.200 \, \text{m} \)
2. **Angular acceleration**, \( \alpha = 2.00 \, \text{rad/s}^2 \)
3. **Time of rotation**, \( t = 4.00 \, \text{s} \)
4. The disk starts from rest, so the **initial angular velocity**, \( \omega_0 = 0 \, \text{rad/s} \).

### Steps to Find Radial (Centripetal) Acceleration
The radial component of acceleration for a point on the rim of the disk is given by:
\[
a_r = \omega^2 \cdot r
\]
where:
- \( \omega \) is the angular velocity at time \( t \),
- \( r \) is the radius of the disk.

#### Step 1: Calculate Angular Velocity, \( \omega \)
Since the disk has constant angular acceleration and starts from rest, we can use the following kinematic equation for angular velocity:
\[
\omega = \omega_0 + \alpha t
\]
Substituting the known values:
\[
\omega = 0 + (2.00 \, \text{rad/s}^2)(4.00 \, \text{s}) = 8.00 \, \text{rad/s}
\]

#### Step 2: Calculate Radial (Centripetal) Acceleration, \( a_r \)
Now that we know \( \omega = 8.00 \, \text{rad/s} \), we can calculate \( a_r \):
\[
a_r = \omega^2 \cdot r = (8.00 \, \text{rad/s})^2 \cdot 0.200 \, \text{m}
\]
\[
a_r = 64 \cdot 0.200 = 12.8 \, \text{m/s}^2
\]

### Answer
The correct answer is:
\[
\boxed{12.8 \, \text{m/s}^2}
\]

Thus, option **(d)** is correct.

Would you like further details or have any questions?

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Here are some related questions to expand your understanding:

1. How would the radial acceleration change if the angular acceleration were doubled?
2. What would the radial acceleration be if the disk rotated for 6.00 seconds instead of 4.00 seconds?
3. What is the relationship between tangential and radial acceleration in this scenario?
4. How would the result change if the disk had a larger radius?
5. What formula would you use to find the tangential acceleration?

**Tip:** Radial (centripetal) acceleration depends on the square of the angular velocity, making it highly sensitive to changes in \( \omega \).

A solid disk with radius 0.200 m is mounted on an axle through its center. It starts from rest and then rotates with constant angular acceleration α = 2.00 rad/s². What is the radial component of the acceleration of a point on the rim of the disk after the disk has rotated for 4.00 s?

Calculate the radial component of the acceleration for a point on the rim of a rotating solid disk with radius 0.200 m and angular acceleration 2.00 rad/s² after 4.00 seconds. This problem demonstrates key concepts in angular motion and centripetal acceleration.

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