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


v = 9 m per sec , r = 5 m

Verified step by step guidance

1. Identify the given values: linear velocity \( v = 9 \) m/s and radius \( r = 5 \) m.
2. Recall the formula for linear velocity in terms of angular velocity: \( v = r \omega \), where \( \omega \) is the angular velocity.
3. Rearrange the formula to solve for the missing variable \( \omega \): \( \omega = \frac{v}{r} \).
4. Substitute the given values into the rearranged formula: \( \omega = \frac{9}{5} \).
5. Simplify the expression to find the angular velocity \( \omega \).

Key Concepts

Linear Velocity (v)

Linear velocity (v) is the rate at which an object moves along a path. In the context of circular motion, it represents the distance traveled per unit of time, typically measured in meters per second (m/s). Understanding linear velocity is crucial for solving problems involving circular motion, as it relates directly to the radius and angular velocity.

Radius (r)

The radius (r) is the distance from the center of a circle to any point on its circumference. In circular motion, the radius plays a significant role in determining the linear velocity of an object moving along the circular path. A larger radius results in a greater distance traveled in the same time frame, affecting the overall speed of the object.

Angular Velocity (ω)

Angular velocity (ω) measures how quickly an object rotates around a central point, expressed in radians per second. It is a key component in the relationship between linear velocity and radius in circular motion, as it helps to determine how fast an object is moving along its circular path. The formula v = rω illustrates this relationship, linking linear and angular motion.