Textbook Question
Give the exact value of each expression. See Example 5. tan 30°
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3. Unit Circle
Defining the Unit Circle
Problem 13
Textbook Question
Use the formula ω = θ/t to find the value of the missing variable.
ω = 0.91 radian per min, t = 8.1 min
Verified step by step guidance1
Identify the given variables and the formula: angular velocity \(\omega = 0.91\) rad/min, time \(t = 8.1\) min, and the formula \(\omega = \frac{\theta}{t}\) where \(\theta\) is the angular displacement in radians.
Rearrange the formula to solve for the missing variable \(\theta\): multiply both sides of the equation by \(t\) to get \(\theta = \omega \times t\).
Substitute the known values into the rearranged formula: \(\theta = 0.91 \times 8.1\).
Perform the multiplication to find the angular displacement \(\theta\) in radians (do not calculate the final value here, just set up the expression).
Interpret the result as the total angle in radians that the object has rotated through in the given time.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Velocity (ω)
Angular velocity measures how fast an object rotates or revolves, expressed in radians per unit time. It indicates the angle covered per unit time, such as radians per minute, and is a fundamental quantity in rotational motion.
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Angular Displacement (θ)
Angular displacement is the angle through which an object has rotated, measured in radians. It represents the change in the angular position of the object and is the product of angular velocity and time when motion is uniform.
Relationship Between Angular Velocity, Displacement, and Time
The formula ω = θ / t relates angular velocity (ω), angular displacement (θ), and time (t). Given any two variables, the third can be found by rearranging the formula, making it essential for solving problems involving rotational motion.
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