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 variables and the unknown variable. Here, the linear velocity \(v = 9\) m/s, the radius \(r = 5\) m, and the angular velocity \(\omega\) is unknown.
2. Recall the formula relating linear velocity, radius, and angular velocity: \(v = r \times \omega\).
3. Rearrange the formula to solve for the missing variable \(\omega\): \(\omega = \frac{v}{r}\).
4. Substitute the known values into the rearranged formula: \(\omega = \frac{9}{5}\).
5. Simplify the expression to find the angular velocity \(\omega\) (do not calculate the final numerical value as per instructions).

Key Concepts

Relationship Between Linear and Angular Velocity

The formula v = r ω connects linear velocity (v) and angular velocity (ω) through the radius (r). It shows that linear velocity is the product of the radius and the angular velocity, describing how fast a point on a rotating object moves along its circular path.

Units and Dimensions in Rotational Motion

In the formula v = r ω, linear velocity (v) is measured in meters per second (m/s), radius (r) in meters (m), and angular velocity (ω) in radians per second (rad/s). Understanding these units helps ensure correct substitution and calculation of the missing variable.

Solving for a Missing Variable in an Equation

To find the missing variable, rearrange the formula algebraically. For example, if ω is unknown, solve ω = v / r. This process requires isolating the variable on one side and substituting known values to compute the result.