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 values: \( \omega = \frac{2\pi}{3} \) radians per second and \( t = 3 \) seconds.
2. Recognize that the formula to use is \( \omega = \frac{\theta}{t} \), where \( \omega \) is the angular velocity, \( \theta \) is the angle in radians, and \( t \) is the time in seconds.
3. Rearrange the formula to solve for \( \theta \): \( \theta = \omega \times t \).
4. Substitute the given values into the rearranged formula: \( \theta = \frac{2\pi}{3} \times 3 \).
5. Simplify the expression to find the value of \( \theta \).

Key Concepts

Angular Velocity (ω)

Angular velocity (ω) is a measure of how quickly an object rotates or moves around a central point, expressed in radians per second. It quantifies the rate of change of the angular position of an object over time. In the given formula, ω represents this rate, allowing us to understand how fast the angle θ changes as time t progresses.

Angular Displacement (θ)

Angular displacement (θ) refers to the angle in radians through which an object has rotated about a specific axis. It is a crucial component in rotational motion, as it indicates the total angle covered during the time interval t. In the context of the formula ω = θ/t, θ is the variable we need to find, given the values of ω and t.

Time (t)

Time (t) in this context represents the duration over which the angular displacement occurs. It is a fundamental variable in the relationship between angular velocity and angular displacement. In the formula ω = θ/t, time is used to determine how long it takes for the object to rotate through the angle θ, allowing us to calculate the missing variable when the other values are known.