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8. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. (i) What is the car's angular speed in radians per hour? (ii) What is the car’s linear speed in miles per hour?

User Magdiel
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2 Answers

6 votes

Answer:

(i) 10 revolutions = 10(2π) = 20π radians

10 revolutions/sec =

(20π radians/sec)(3,600 sec/hr) =

72,000π radians/hr

(ii) C = 18π inches

10 revolutions × 18π inches =

180π inches

(180π in./sec)(3,600 sec/hr) =

(648,000π in./hr)(1 mi./63,360 in.)

= 225π/22 miles/hour

= about 32.13 miles/hour

User MrHant
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4 votes

Answer:

the car's angular speed is 72,000π radians per hour.

the car's linear speed is approximately 100.53 miles per hour.

Explanation:

To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.

The formula for angular speed is:

ω = 2πf

where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.

In this case, the wheel is spinning at a rate of 10 revolutions per second, so:

ω = 2π(10) = 20π radians per second

To convert this to radians per hour, we can multiply by the number of seconds per hour:

20π radians per second × 3600 seconds per hour = 72,000π radians per hour

To find the car's linear speed in miles per hour, we can use the formula:

v = rω

where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.

The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:

9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles

Now we can substitute the values we have found:

v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)

v ≈ 100.53 miles per hour

User Wubbalubba
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