The problem in the image asks to calculate the tangential (linear) velocity of an object being rotated with a string of 0.5 meters in length, and an angular velocity of 24 rad/s. The question is to find the speed at which the object moves.

Solution:

To find the tangential velocity $v$ of an object rotating in a circular path, we use the formula: $v = r \cdot \omega$ where:

• $r$ is the radius of the circular path (0.5 meters in this case),
• $\omega$ is the angular velocity (24 rad/s).

Plugging in the values: $v = 0.5 \, \text{m} \times 24 \, \text{rad/s} = 12 \, \text{m/s}$

Answer:

The correct answer is C. 12 m/s.

Would you like further explanation or have any questions on this topic?

Here are five related questions to expand on this concept:

1. What is the relationship between tangential velocity and angular velocity?
2. How would the tangential velocity change if the radius was doubled?
3. What is the difference between angular velocity and linear velocity?
4. How do you calculate the centripetal acceleration of a rotating object?
5. What units are typically used for angular velocity, and why?

Tip:

Remember, tangential velocity is directly proportional to both the radius of rotation and the angular velocity. If either of these increases, the tangential velocity will also increase.