Find the linear speed v for each of the following.

Question

the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m)

Accepted Answer

Welcome back. I am so glad you're here. We're told that a prototype of a car wheel has a diameter of 15 centimeters during testing. It rotates at 750 times or revolutions per minute. Calculate the linear speed V of a point on the outermost surface of the car wheel. Our answer choices are answer choice. A 3765 pi centimeters per minute. Answer choice. B 14,350 pi centimeters per minute. Answer choice. C 5625 pi centimeters per minute and answer choice. D 11,250 pi centimeters per minute. All right. So we recall from previous lessons that our linear speed can be found with the equation V equals R omega where R is our radius? An omega is our angular speed. So can we figure out our radius and our angular speed? Well, the radius is the distance from the center to the edge. And if we know that the diameter from one edge to the other passing through the center is 15 centimeters here, the diameter divided by two or 15 centimeters divided by two is going to be our radius. So 15 centimeters divided by two is 7.5 centimeters, that's our radius. Now, how about our angular speed? We recall from previous lessons that angular speed is theta divided by T. So that's our radiance divided by our unit of time. Here, we know we're talking about minutes, but we don't have it measured in terms of radiance. We have it measured in terms of revolutions. If we were to take our revolutions, though, we can translate that into radiance. We know that once around the circle is two pi. So in other words, one revolution once around the circle equals two pi radians. And we can use unit conversion to take our 750 revolutions per minute and turn it into radians per minute. So we'll multiply this by, we'll put two pi radiance in the numerator divided by one revolution multiplying that by the 750 revolutions per minute, our revolutions cancel out and multiplying straight across 750 multiplied by two pi is 1500 pi and our units are radians per minute. All right. So now we have our angular speed. It's 1500 pi radians per minute. Now, we can go back to our v our linear speed and solve. So we'll multiply our radius 7.5 centimeters by our angular speed. 1500 pi radians per minute, multiplying straight across 7.5 multiplied by 1500 is 11,250. And that's still pi then we have our units, well, we have centimeters and radiance in the numerator. But linear speed is given in terms of distance divided by time. So we can disregard the radiance and it's just going to be centimeters, the distance divided by time, the minutes. And that is our linear speed. 1 11,250 pi centimeters per minute. We look at our answer choices and that matches with answer choice. D well done. We'll catch you on the next one.

Find the linear speed v for each of the following.

the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m)

Key Concepts

Angular Velocity

Radius in Circular Motion

Linear Speed in Circular Motion

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