A car with a wheel of radius 14 inches is moving with a speed of 55 mph. Find the angular speed of the automobile to the nearest mile per hour.

I got 55/14

You've got to see that dividing 55mi/hr by 14in is a useless amount.

try to do a sanity check on your answer. Just because you have a number doesn't mean it's correct, or even reasonable.

55/14 is about 4. Surely you don't think a car going 55 mph has its wheels turning at 4 rev/hr!

Angular speed is measured in radians/sec. Since a full circle has 2pi radians, the angular speed is 2pi times the speed in rev/sec.

To get rev/sec, divide the distance traveled by the circumference of the wheel.

55 mi/hr * 5280ft/mi * 12in/ft * 1hr/3600sec = 968 in/sec

2pi*14 = 28pi in/rev

so, the angular speed is 968/28pi = 242/7pi rev/sec

Now multiply that by 2pi to get

484/7 radians/sec

angular speed would have to be expressed as units of angle per unit of time, e.g. so many rotations per minute, or rpm.

It would not be measured in miles per hour

the circumference of the wheel is 2(14)π = 28π inches
55 mph = 55(5280)(12)
or 3484800 inches/hour
= 58080 inches/minute

so the angular speed = 58080/28π rotations per minute
= appr 660.27 rotations/min

your answer of 55/14 is totally meaningless
what units would it be in ??

Sorry the problem states find the angular speed of the wheel, not the car, in radians per second.

The way I derived my answer was through the linear speed formula (v = radius * angular speed) and so plugging in would yield (55 = 14x), but I do understand some conversions would be necessary.

Oh, I see you're asking about the angular speed of the car. Well, to find that, we need to convert the linear speed in miles per hour (mph) to angular speed in radians per hour. The formula for the angular speed is given by:

Angular Speed = Linear Speed / Radius

In this case, the linear speed is 55 mph, and the radius is 14 inches. Let's convert the inches to miles first, because those little inches need to stretch a bit! There are 12 inches in a foot and 5280 feet in a mile, so:

(14 inches / 12) feet * (1 mile / 5280 feet) = 0.001325 miles

Now we can plug these values into the formula:

Angular Speed = 55 mph / 0.001325 miles

Calculating this, I got approximately 41,509 radians per hour. But wait, we need to round this to the nearest mile per hour! So, my dear friend, the angular speed of the car is approximately 41,509 miles per hour (mph). Just keep in mind that this is a conversion from radians to miles. Don't try to outrun the speed of light with this one!

To find the angular speed of the car, we need to convert its linear speed to angular speed. The linear speed is given in mph (miles per hour), and the angular speed is typically measured in radians per hour.

To convert from linear speed to angular speed, we can use the formula:

Angular speed = Linear speed / Radius

In this case, the radius is given as 14 inches. However, we need to convert it to miles since the linear speed is given in mph. There are 63360 inches in a mile, so the radius in miles would be:

14 inches * (1 mile / 63360 inches) = 0.00022047 miles

Now, we can substitute the values into the formula:

Angular speed = 55 mph / 0.00022047 miles

Calculating this value, the angular speed of the car is approximately 249,053 radians per hour.

Therefore, the angular speed of the automobile is approximately 249,053 radians per hour to the nearest mile per hour.