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


θ = 2π/9 radian , ω = 5π/27 radian per min

Verified step by step guidance

1. Identify the given values: \( \theta = \frac{2\pi}{9} \) radians and \( \omega = \frac{5\pi}{27} \) radians per minute.
2. Recall the formula for angular velocity: \( \omega = \frac{\theta}{t} \).
3. Rearrange the formula to solve for the missing variable \( t \): \( t = \frac{\theta}{\omega} \).
4. Substitute the given values into the rearranged formula: \( t = \frac{\frac{2\pi}{9}}{\frac{5\pi}{27}} \).
5. Simplify the expression by dividing the fractions: \( t = \frac{2\pi}{9} \times \frac{27}{5\pi} \).

Key Concepts

Angular Displacement (θ)

Angular displacement, represented by θ, measures the angle through which an object has rotated about a fixed point. It is typically expressed in radians, where one complete revolution corresponds to 2π radians. In this question, θ is given as 2π/9 radians, indicating a specific fraction of a full rotation.

Angular Velocity (ω)

Angular velocity, denoted by ω, quantifies the rate of change of angular displacement over time. It is expressed in radians per unit time, such as radians per minute. In the provided question, ω is given as 5π/27 radians per minute, indicating how quickly the object is rotating.

Time (t)

Time (t) in the context of angular motion refers to the duration over which the angular displacement occurs. It is a crucial variable in the formula ω = θ/t, as it allows us to relate the angular displacement to the angular velocity. By rearranging the formula, we can solve for the missing time variable when the other two are known.