A sphere is rolled on a rough horizontal surface. It gradually slows down and stops. The force of friction tries to

Options

A. decrease the linear velocity
B. increase the angular velocity
C. increase the linear momentum
D. decrese the angular velocity

Answer

To solve the question, we need to analyze the motion of a sphere rolling on a rough horizontal surface and understand the role of friction in this scenario.

### Step-by-Step Solution:

1. **Understanding the Motion of the Sphere:**
- The sphere is rolling on a rough surface, which means it is undergoing both translational (linear) and rotational motion.
- The center of mass of the sphere has a linear velocity \( v_c \), and the point of contact with the ground has a velocity of zero when rolling without slipping.

2. **Identifying the Forces Acting on the Sphere:**
- As the sphere rolls, the force of friction acts at the point of contact.
- Since the sphere is gradually slowing down and eventually stops, the frictional force must act in the opposite direction to the linear motion of the sphere.

3. **Direction of Friction:**
- The linear velocity \( v_c \) is directed forward. Therefore, the force of friction must act backward to oppose this motion.
- This backward frictional force will reduce the linear velocity of the sphere.

4. **Effect of Friction on Linear Velocity:**
- Since the friction acts in the opposite direction to the linear velocity, it will decrease the linear velocity \( v_c \) of the sphere over time until it comes to a stop.

5. **Effect of Friction on Angular Velocity:**
- The sphere also has an angular velocity \( \omega \) due to its rotation. The point of contact has a linear velocity of \( R\omega \) (where \( R \) is the radius of the sphere).
- As the friction acts in the backward direction, it also contributes to the rotation of the sphere. This means that while the linear velocity decreases, the angular velocity will increase because the frictional force helps in maintaining the rolling motion.

6. **Conclusion:**
- The force of friction decreases the linear velocity of the sphere and increases the angular velocity.
- Therefore, the correct statements regarding the effects of friction are:
- A: The force of friction decreases the linear velocity.
- B: The force of friction increases the angular velocity.
- C: The force of friction does not increase the linear momentum; it decreases it.
- D: The force of friction does not decrease the angular velocity; it increases it.

### Final Answer:
The force of friction tries to:
- A: Decrease the linear velocity.
- B: Increase the angular velocity.