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To find the linear speed given the angular speed, we can use the relationship between linear speed \( v \), angular speed \( \omega \), and the radius \( r \) of the circle:

\[
v = \omega \times r
\]

In this problem:

- The angular speed \( \omega \) is given as \( \pi \) radians per second.
- Since point \( P \) is moving along the *unit circle*, the radius \( r = 1 \).

Now we can substitute these values into the formula:

\[
v = \pi \times 1 = \pi
\]

Therefore, the linear speed of point \( P \) is \( \pi \) units per second.

If you need further details or have any questions, feel free to ask.

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Here are five related questions that expand on this topic:

1. What is the relationship between angular and linear speed for different radii?
2. How would the linear speed change if the radius were doubled but the angular speed remained the same?
3. How can we convert between linear speed and angular speed if the radius is unknown?
4. What units are typically used for angular and linear speeds, and how do they relate to each other?
5. How would you calculate the distance traveled by point \( P \) in a given time?

**Tip:** Remember that linear speed on a circular path depends directly on the radius; doubling the radius doubles the linear speed for the same angular velocity.

If the angular speed of point P is π radians per second, then the linear speed is ______ unit(s) per sec.

Learn how to calculate the linear speed of a point moving along a unit circle when the angular speed is π radians per second. This problem explores concepts in circular motion, including the relationship between angular and linear speed.

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