The image shows a physics question written in Arabic that involves circular motion.

Translation and interpretation of the question: "A body moves in a circular path with a radius of 100 cm (0.1 meters). Its period is 2 seconds. What is the magnitude of its linear velocity in m/s?"

The formula for linear velocity $v$ in circular motion is:

$v = \omega r$

where:

• $v$ is the linear velocity,
• $\omega$ is the angular velocity, and
• $r$ is the radius of the circular path.

1. Find the angular velocity $\omega$:

The angular velocity is related to the period $T$ by:

$\omega = \frac{2\pi}{T}$

Given $T = 2$ seconds:

$\omega = \frac{2\pi}{2} = \pi \, \text{rad/s}$

2. Now calculate the linear velocity $v$:

$v = \omega r$

Given that the radius $r = 0.5$ meters (half of the diameter):

$v = \pi \times 0.5 = 1.57 \, \text{m/s}$

Thus, the linear velocity is approximately $1.57 \, \text{m/s}$.

Do you need further details on any part of the solution?

Here are 5 related questions to deepen your understanding:

1. How is the angular velocity related to the frequency of circular motion?
2. What would happen to the linear velocity if the period was halved?
3. How can you calculate the total distance traveled by the body in one complete revolution?
4. How does the linear velocity change if the radius of the circular path is doubled?
5. What is the difference between linear velocity and angular velocity in circular motion?

Tip: Remember that angular velocity $\omega$ is constant for uniform circular motion, while linear velocity depends on the radius of the circle.