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


θ = 3π/4 radians, t = 8 sec

Verified step by step guidance

1. Identify the given values: \( \theta = \frac{3\pi}{4} \) radians and \( t = 8 \) seconds.
2. Recall the formula for angular velocity: \( \omega = \frac{\theta}{t} \).
3. Substitute the given values into the formula: \( \omega = \frac{\frac{3\pi}{4}}{8} \).
4. Simplify the expression by dividing the numerator by the denominator: \( \omega = \frac{3\pi}{4 \times 8} \).
5. Further simplify the expression: \( \omega = \frac{3\pi}{32} \).

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 2π radians correspond to a full rotation (360 degrees). In this question, θ is given as 3π/4 radians, indicating that the object has rotated three-quarters of the way around a circle.

Time (t)

Time (t) in this context refers to the duration over which the angular displacement occurs. It is a crucial variable in calculating angular velocity, as it provides the timeframe for the rotation. In the question, t is specified as 8 seconds, which will be used to determine how quickly the object is rotating.

Angular Velocity (ω)

Angular velocity (ω) is a measure of how quickly an object rotates around a point, defined as the rate of change of angular displacement over time. It is calculated using the formula ω = θ/t, where θ is the angular displacement and t is the time taken. In this case, substituting the given values will yield the angular velocity in radians per second.