The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.

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Identify the given information: the propeller rotates at 5000 revolutions per minute (rpm). We need to find the angular speed in radians per second.

Recall the relationship between revolutions and radians: one revolution corresponds to \(2\pi\) radians.

Convert revolutions per minute to radians per minute by multiplying the number of revolutions by \(2\pi\): angular speed in radians per minute = \(5000 \times 2\pi\).

Convert the angular speed from radians per minute to radians per second by dividing by 60, since there are 60 seconds in one minute: angular speed in radians per second = \(\frac{5000 \times 2\pi}{60}\).

Simplify the expression if needed to express the angular speed 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 Speed

Angular speed measures how fast an object rotates or revolves, expressed as the angle covered per unit time. It is commonly measured in radians per second, representing the rate of change of angular displacement.

Conversion from Revolutions per Minute to Radians per Second

To convert revolutions per minute (rpm) to radians per second, multiply by 2π (radians in one revolution) and divide by 60 (seconds in a minute). This conversion translates rotational speed into standard angular velocity units.

Relationship Between Horsepower and Rotational Speed

While horsepower indicates the power output of the motor, it does not directly affect the angular speed calculation. Understanding this distinction helps focus on rotational speed data (rpm) for angular velocity conversion.

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