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


v = 12 m per sec, ω = 3π/2 radians per sec

Verified step by step guidance

1. Identify the given values: \( v = 12 \text{ m/s} \) and \( \omega = \frac{3\pi}{2} \text{ radians/s} \).
2. Recall the formula for linear velocity: \( v = r \omega \), where \( v \) is the linear velocity, \( r \) is the radius, and \( \omega \) is the angular velocity.
3. Rearrange the formula to solve for the missing variable \( r \): \( r = \frac{v}{\omega} \).
4. Substitute the known values into the rearranged formula: \( r = \frac{12}{\frac{3\pi}{2}} \).
5. Simplify the expression to find the value of \( r \).

Key Concepts

Linear Velocity (v)

Linear velocity (v) is the rate at which an object moves along a path. In circular motion, it is defined as the distance traveled per unit of time, typically measured in meters per second (m/s). In this context, v represents the linear speed of a point on the circumference of a circle.

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 through which an object rotates in a given time frame. In the formula v = rω, ω is crucial for relating linear speed to the radius of the circular path.

Radius (r)

The radius (r) is the distance from the center of a circle to any point on its circumference. In the context of the formula v = rω, the radius is essential for determining the relationship between linear and angular velocity. A larger radius results in a higher linear velocity for the same angular velocity.