It takes 0.7 s for the ball to go around the circle once. The circle has a radius of 0.4 m. what is its velocity

The velocity of an object moving in a circular path can be calculated using the formula for **tangential velocity**:

\[
v = \frac{2 \pi r}{T}
\]

where:
- \(v\) is the velocity,
- \(r\) is the radius of the circle,
- \(T\) is the period (time it takes to complete one full revolution),
- \(\pi \approx 3.1416\).

Given:
- The radius \(r = 0.4 \, \text{m}\),
- The period \(T = 0.7 \, \text{s}\).

Now, we can plug in the values:

\[
v = \frac{2 \pi (0.4)}{0.7} = \frac{2.513}{0.7} \approx 3.59 \, \text{m/s}
\]

Thus, the velocity of the ball is approximately **3.59 m/s**.

Would you like further clarification or details on this? 

Here are some related questions to deepen your understanding:
1. How would the velocity change if the radius were doubled?
2. What would happen to the velocity if the period were halved?
3. What is the relationship between angular velocity and tangential velocity?
4. Can you derive the acceleration for this circular motion?
5. How does centripetal force relate to this problem?

**Tip:** In circular motion, tangential velocity is directly proportional to the radius for a given period.

It takes 0.7 s for the ball to go around the circle once. The circle has a radius of 0.4 m. What is its velocity?

Learn how to calculate the tangential velocity of a ball moving in a circular path with a radius of 0.4 m and a period of 0.7 s. This solution covers key concepts such as tangential velocity and circular motion, using the formula v = 2πr / T. Suitable for students in Grades 9-12.

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