The propeller of a 90-horsepower outboard motor at full thrott...

Question

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.

Accepted Answer

Welcome back. I am so glad you're here. We're told that a gear we're going to draw it as a circle underneath a moving walkway at an airport in Amsterdam rotates at 230 revolutions per minute. We are asked to calculate its angular speed in radiance per second and express the answer to the nearest 10th. Our answer choices are answer choice. A 24.1 radiance per second. Answer choice B 39.8 radiance per second. Answer choice C 22.7 radiance per second and answer choice D 34.4 radians per second. All right. So we're looking for angular speed, angular speed is omega and that's expressed in terms of the divided by T or radiance per unit of time. And we are given instructions to find it in time per second, but we're given something in revolutions per minute. So we're in the wrong units, 230 revolutions per minute is very close to being radians per second. We can get there because we know that one revolution once around the circle is equal to, to pi radiance once around the circle. And we also know that one minute is equal to 60 seconds. So we can use unit conversion in order to get this into radians per second. So we want the revolutions to cancel out. So we'll multiply this by the unit where we have two pi radians in the numerator divided by one revolution. And then we want the minutes to cancel out. So we'll put one minute in the numerator for a new unit and that's divided by 60 seconds. And now our revolutions cancel out and our minutes cancel out and we can just multiply straight across and simplify. So 230 multiplied by two pi multiplied by one will give us 460 pi. And for our units in the numerator, we have radiance in the denominator for numbers, we've got 60 for our units, we have seconds. So 460 pi divided by 60 radians per second, we are asked to express the answer to the nearest 10th. So on the calculator, we can take 460 pi divided by 60. And that gives us approximately 24.08 which rounds to the nearest 10th as 24.1. And that is radiance per second. And there is our angular speed. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

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.

Key Concepts

Angular Speed

Conversion from Revolutions per Minute to Radians per Second

Relationship Between Horsepower and Rotational Speed

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