An object is moving in a circular path of radius 4.00 m. If the object moves through an angle of 1.2 radians, then the tangential distance traveled by the object is

To calculate the tangential distance traveled by an object moving in a circular path, we use the formula for arc length:

\[
\text{Arc Length} (s) = r \times \theta
\]

where:
- \( r \) is the radius of the circular path (4.00 m),
- \( \theta \) is the angle in radians (1.2 radians).

Now, substituting the values:

\[
s = 4.00 \, \text{m} \times 1.2 \, \text{radians} = 4.8 \, \text{m}
\]

Thus, the tangential distance traveled by the object is **4.8 meters**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the relation between angular velocity and tangential velocity?
2. How would the distance change if the radius were doubled?
3. What is the angular displacement in degrees for 1.2 radians?
4. How does centripetal force affect the motion in a circular path?
5. What happens to the motion if the object accelerates tangentially?

**Tip:** The arc length is directly proportional to both the radius and the angle in radians, so small changes in either can affect the tangential distance significantly.

Discover how to calculate the tangential distance traveled by an object moving in a circular path with a radius of 4.00 meters and an angle of 1.2 radians. This problem explores key geometric concepts and the arc length formula. Suitable for students in Grades 9-10.

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