Use the formula v = r ω to find the value of the missing variable.


r = 12 m , ω = 2π/3 radians per sec

Verified step by step guidance

1. Identify the given values: radius \( r = 12 \) meters and angular velocity \( \omega = \frac{2\pi}{3} \) radians per second.
2. Recall the formula for linear velocity: \( v = r \cdot \omega \).
3. Substitute the given values into the formula: \( v = 12 \cdot \frac{2\pi}{3} \).
4. Simplify the expression by multiplying the numbers: \( v = 12 \times \frac{2\pi}{3} \).
5. Complete the multiplication to find the linear velocity \( v \).

Key Concepts

Angular Velocity (ω)

Angular velocity (ω) measures how quickly an object rotates around a central point, expressed in radians per second. It indicates the angle covered per unit of time, allowing us to understand the rotational speed of an object. In this question, ω is given as 2π/3 radians per second, which is essential for calculating linear velocity.

Radius (r)

The radius (r) is the distance from the center of a circle to any point on its circumference. In the context of circular motion, the radius plays a crucial role in determining the linear velocity of an object moving along a circular path. Here, the radius is provided as 12 meters, which is necessary for applying the formula v = rω.

Linear Velocity (v)

Linear velocity (v) represents the speed of an object moving along a circular path and is calculated using the formula v = rω. This formula shows that linear velocity is directly proportional to both the radius and the angular velocity. By substituting the given values of r and ω into this formula, we can find the missing variable, which is the linear velocity.