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The image presents a problem involving a spinning basketball on a finger, where points \( P \) and \( Q \) on the surface of the ball are being analyzed for their motion characteristics. The problem asks which of the following is true about the points \( P \) and \( Q \):

A. 半径相等 (Equal radii)
B. 线速度大小相等 (Equal linear speeds)
C. 向心加速度大小相等 (Equal centripetal accelerations)
D. 角速度大小相等 (Equal angular speeds)

To solve this, we need to analyze the motion of points on a rotating sphere. 

1. **Equal Radii**: This is not relevant to the motion characteristics we are comparing (thus option A is irrelevant).
   
2. **Equal Linear Speeds**: The linear speed \( v \) of a point on a rotating object is given by \( v = \omega r \), where \( \omega \) is the angular speed and \( r \) is the radius from the axis of rotation. Points \( P \) and \( Q \) are at different distances from the axis of rotation, thus they do not have equal linear speeds (option B is incorrect).

3. **Equal Centripetal Accelerations**: The centripetal acceleration \( a_c \) is given by \( a_c = \omega^2 r \). Since points \( P \) and \( Q \) are at different radii from the axis of rotation, they will have different centripetal accelerations (option C is incorrect).

4. **Equal Angular Speeds**: Every point on a rigid body rotates with the same angular speed \( \omega \). Therefore, the points \( P \) and \( Q \) must have the same angular speed (option D is correct).

Hence, the correct answer is:

D. 角速度大小相等 (Equal angular speeds)

Would you like further details on any aspect of this explanation?

Here are five questions you can ask next:
1. How do you calculate the linear speed of a point on a rotating object?
2. What is the relationship between angular speed and centripetal acceleration?
3. How do you determine the radius for points on a rotating sphere?
4. Can two points on a rotating body have different angular velocities?
5. What factors affect the centripetal force on a rotating object?

**Tip:** When analyzing rotational motion, always consider both linear and angular quantities, as they provide different insights into the motion.

Explore the rotational motion problem involving points P and Q on a spinning basketball. Understand concepts such as angular speed and centripetal acceleration through detailed analysis. Suitable for advanced high school students.

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