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Problem 14

Angular Speed A car is moving at the rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet.

(a) Find the number of revolutions per minute that the wheels are rotating.

(b) Find the angular speed of the wheels in radians per minute.

Answer

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## Discussion

## Video Transcript

team tells us that a car is moving at a rate of 50 miles per hour, and the diameter of each of its wheels is 2.5 feet. The first part, eh? We're supposed to find the number of revolutions per minute that the wheels are rotating, and then in Part B, we need to find the angular speed of the wheels and radiance permanent. So over here I've drawn our wheel. You see, it's on Landon's rotating. Let's first begin by notated ing where that diameter is and then given a label of the and it's 2.5 feet. Now, in part A. We need to convert from our 15 miles per hour all the way to, um, Revolutions permanent. And so to do that, we're gonna set up a couple conversion factors we're just gonna multiply through and will eventually end up with revolutions per minute. So what we know is that our diameters given to us and feet and we can use our diameter to solve for the circumference of our wheel. And as I'm wheel moves along, it's gonna rotate and traverse the distance over circumference many, many times, every single time. It is a complete rotation, it will travel the distance of our circumference. And so that's the key fact. We wantto leverage when we find our solution. So let's get our miles converted in defeat. One mile is the same is 5280 feet. And here's the way we're going to use that conversion factor that relates the diameter to the circumference. So we say that 2.5 times hi feet because the circumference is just the high times, the diameter is the same as one revolution. So we have revolutions in our numerator, and that's what we wanted the miles that he cancel out. Now we want to get that as revolutions per minute, not revolutions per hour. So over here will come over here and we'll write. One hour is the same as 60 minutes, and if we look at our conversion factors, we find miles. Cancel out hours, cancel out feet, cancels out, and we're left with revolutions per minute. So go ahead. There's a multiply through, and we'll find that the answer is approximately or pretty darn close. Two, 1120 0.5 rpm. Our revolution's permanent, so that's the solution for party now moving on to Part B, We want to find the angular speed of the wheels and radiance per minute and so we can use the answer that we just got up here to solve for B. So we have 1120.5 revolutions for one minute, and we want to find the speed of the wheels and radiance per minute. Well, one complete revolution of a circle is the same as two pi radiance. So we can eye one rev equals two pi rad. We see revolutions cancel on. We're left with rads per minute, which is the desired units we wanted. And using our calculator, we find that that is the same as 7000 and 40 rads for a minute. And there you have it. You have found the speeds of these wheels and repetitions per minute, revolutions permanent and radiance permanent

## Recommended Questions

ANGULAR SPEED A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet.

(a) Find the number of revolutions per minute the wheels are rotating.

(b) Find the angular speed of the wheels in radians per minute.

ANGULAR SPEED A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet.

(a) Find the number of revolutions per minute the wheels are rotating.

(b) Find the angular speed of the wheels in radians per minute.

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(a) Find the angular speed of the carousel in radians per minute.

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If a car travels at a speed of 60 miles per hour, find the angular speed (in radians per second) of a tire that has a diameter of 2 feet.

A motorcycle wheel has a diameter of 19.5 inches (see figure) and rotates at 1050 revolutions per minute.

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You are given the rate of rotation of a wheel as well as its radius. In each case, determine the following: (a) the angular speed, in units of radians/sec; (b) the linear speed, in units of cm/sec, of a point on the circumference of the wheel; and (c) the linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference.

1080^{\circ} / \mathrm{sec} ; r=25 \mathrm{cm}

You are given the rate of rotation of a wheel as well as its radius. In each case, determine the following: (a) the angular speed, in units of radians/sec; (b) the linear speed, in units of cm/sec, of a point on the circumference of the wheel; and (c) the linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference.

$1250 \mathrm{rpm} ; r=10 \mathrm{cm}$

Angular Speed A computerized spin balance machine rotates a 25 -inch diameter tire at 480 revolutions per minute.

(a) Find the road speed (in miles per hour) at which the tire is being balanced.

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