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

θ = 3π/4 radians, t = 8 sec

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Identify the given variables and the formula: angular displacement \(\theta = \frac{3\pi}{4}\) radians, time \(t = 8\) seconds, and the formula for angular velocity \(\omega = \frac{\theta}{t}\).

Substitute the known values into the formula: \(\omega = \frac{\frac{3\pi}{4}}{8}\).

Simplify the expression by dividing the numerator by the denominator: \(\omega = \frac{3\pi}{4} \times \frac{1}{8}\).

Multiply the fractions: \(\omega = \frac{3\pi}{4 \times 8} = \frac{3\pi}{32}\).

Express the final formula for angular velocity \(\omega\) in terms of \(\pi\) and seconds, which represents the angular velocity in radians per second.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angular Displacement (θ)

Angular displacement represents the angle through which an object rotates, measured in radians. It indicates the change in the angular position of the object and is essential for calculating angular velocity.

Time Interval (t)

Time interval is the duration over which the angular displacement occurs, measured in seconds. It is a key variable in determining the rate of rotation or angular velocity.

Angular Velocity (ω)

Angular velocity is the rate of change of angular displacement with respect to time, expressed in radians per second. It is calculated using the formula ω = θ / t, linking angular displacement and time.

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