In uniform circular motion, several key characteristics can help determine which of the statements are true. Let's analyze each one:

1. The stone is moving with constant velocity.

   • False. In uniform circular motion, the magnitude of velocity (speed) remains constant, but the direction changes continuously. Since velocity is a vector quantity (with both magnitude and direction), the velocity is not constant.

2. The change in direction of the stone's motion is due to the centripetal force acting on the stone.

   • True. Centripetal force acts toward the center of the circular path, continuously changing the direction of the stone's velocity to keep it moving in a circle.

3. The direction of the stone's velocity changes as it moves around the circle.

   • True. The velocity vector of the stone points tangentially to the circle and changes direction as the stone moves around, though its magnitude remains constant.

4. The magnitude of the stone's velocity does not change.

   • True. In uniform circular motion, the speed (magnitude of velocity) remains constant, even though the direction of velocity changes.

5. The stone's speed is constant.

   • True. Speed is the scalar magnitude of velocity, and in uniform circular motion, this remains constant.

Summary of Correct Statements

The correct statements for this situation are:

• The change in direction of the stone's motion is due to the centripetal force acting on the stone.
• The direction of the stone's velocity changes as it moves around the circle.
• The magnitude of the stone's velocity does not change.
• The stone's speed is constant.

Would you like a further breakdown on any of these points or a specific aspect of circular motion?

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Here are some related questions that might enhance understanding:

1. How does centripetal acceleration relate to the speed and radius of circular motion?
2. Why is centripetal force required to maintain circular motion?
3. How would the stone’s motion differ if the centripetal force suddenly disappeared?
4. What is the difference between speed and velocity in this context?
5. How does the concept of inertia relate to the stone's motion?

Tip: Remember, in circular motion, velocity is always changing due to the continuous change in direction, even if speed is constant.