Textbook Question
Solve each problem. See Example 6. Rotating Pulley A pulley rotates through 75° in 1 min. How many rotations does the pulley make in 1 hr?
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1. Measuring Angles
Angles in Standard Position
2:43 minutesProblem 5
Textbook Question
Solve each problem. Rotating Propeller The propeller of a speedboat rotates 650 times per min. Through how many degrees does a point on the edge of the propeller rotate in 2.4 sec?
Verified step by step guidance1
Identify the given information: the propeller rotates 650 times per minute, and we want to find the degrees rotated in 2.4 seconds.
Convert the time from seconds to minutes because the rotation rate is given per minute. Use the conversion: \(2.4 \text{ seconds} = \frac{2.4}{60} \text{ minutes}\).
Calculate the number of rotations in 2.4 seconds by multiplying the rotations per minute by the time in minutes: \(\text{rotations} = 650 \times \frac{2.4}{60}\).
Recall that one full rotation corresponds to 360 degrees. To find the total degrees rotated, multiply the number of rotations by 360: \(\text{degrees} = \text{rotations} \times 360\).
Combine all steps to express the total degrees rotated in 2.4 seconds as \(650 \times \frac{2.4}{60} \times 360\), which you can simplify to find the final answer.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Velocity
Angular velocity measures how fast an object rotates, typically expressed in revolutions per minute (rpm) or radians per second. It indicates the number of complete rotations an object makes in a given time, which is essential for converting rotations into angular displacement.
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Unit Conversion Between Time and Rotations
To solve rotation problems, it's crucial to convert time units consistently, such as from minutes to seconds, and relate rotations per minute to rotations over a specific time interval. This allows calculation of the total number of rotations in the given time.
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Conversion Between Rotations and Degrees
One full rotation corresponds to 360 degrees. To find the angular displacement in degrees, multiply the number of rotations by 360. This conversion translates rotational motion into angular measurement, which is the problem's required output.
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