Use the formula ω = θ/t to find the value of the missing variable.


ω = 2π/3 radians per sec, t = 3 sec

Verified step by step guidance

1. Identify the given variables and the formula: angular velocity \(\omega = \frac{\theta}{t}\), where \(\omega\) is angular velocity, \(\theta\) is the angular displacement in radians, and \(t\) is the time in seconds.
2. Substitute the known values into the formula: \(\omega = \frac{2\pi}{3}\) radians per second and \(t = 3\) seconds.
3. Rewrite the formula to solve for the missing variable \(\theta\): multiply both sides of the equation by \(t\) to get \(\theta = \omega \times t\).
4. Plug in the known values into the rearranged formula: \(\theta = \left(\frac{2\pi}{3}\right) \times 3\).
5. Simplify the expression to find \(\theta\), which represents the angular displacement in radians.

Key Concepts

Angular Velocity (ω)

Angular velocity measures how fast an object rotates or revolves, expressed in radians per second. It is the rate of change of angular displacement over time, indicating how many radians the object covers each second.

Angular Displacement (θ)

Angular displacement is the angle through which an object has rotated, measured in radians. It represents the total change in the angular position of the object during a given time interval.

Relationship Between Angular Velocity, Angular Displacement, and Time

The formula ω = θ / t relates angular velocity (ω), angular displacement (θ), and time (t). It shows that angular velocity equals the angular displacement divided by the time taken, allowing calculation of any one variable if the other two are known.