A car is moving at a rate of 65 miles per housr and the diameter of it's wheels is 2.5ft. Find the number of revolutions per minute the wheels are rotating.
I have no idea where to begin on this question. How do you find rev per min?? Can someone walk me step by step how to answer a problem this?
Well, to find the number of revolutions per minute the wheels are rotating, we need to use a little bit of math and some imagination! Let's break it down:
Step 1: Find the circumference of the wheel.
The circumference is the distance around the wheel, which is equal to 2 times π (pi) times the radius of the wheel. Since the diameter is given, we can find the radius by dividing it by 2. So, the circumference is:
C = 2πr, where r is the radius.
C = 2π(2.5/2) ft
C = π (3.14) x 1.25 ft
C ≈ 3.93 ft (rounded to two decimal places)
Step 2: Find the distance the car travels per minute.
Since the car is moving at a rate of 65 miles per hour, to find the distance traveled per minute, we divide it by 60 (since there are 60 minutes in an hour):
Distance per minute = 65 miles / 60 minutes
Distance per minute ≈ 1.08 miles/minute (rounded to two decimal places)
Step 3: Find the number of revolutions per minute.
To find the number of revolutions per minute, we can divide the distance the car travels per minute by the circumference of the wheel:
Revolutions per minute = Distance per minute / Circumference
Revolutions per minute ≈ 1.08 miles/minute / 3.93 ft
Revolutions per minute ≈ 0.0022 miles/minute/ft
And there you have it! The number of revolutions per minute the wheels are rotating is approximately 0.0022 miles/minute/ft. Now, go ahead and impress your friends with your newfound knowledge of car wheels and their rotations!
To find the number of revolutions per minute the wheels are rotating, you can use the formula:
Revolutions per minute (rpm) = Speed (distance per unit of time) / Circumference of the wheel
Step 1: Convert the speed from miles per hour to feet per minute.
1 mile = 5280 feet
1 hour = 60 minutes
Therefore, 65 miles per hour is equal to:
65 miles/hour * 5280 feet/mile * 1 hour/60 minutes = 5720 feet/minute
Step 2: Find the circumference of the wheel.
The diameter of the wheel is given as 2.5 feet. The circumference of a wheel can be calculated using the formula:
Circumference = π * Diameter
where π is approximately 3.14159.
Circumference = 3.14159 * 2.5 feet = 7.85398 feet
Step 3: Calculate the number of revolutions per minute.
Using the formula mentioned earlier:
Revolutions per minute (rpm) = Speed / Circumference
Revolutions per minute = 5720 feet/minute / 7.85398 feet = 729.44
Therefore, the wheels are rotating at approximately 729.44 revolutions per minute.
To find the number of revolutions per minute that the wheels of the car are rotating, we need to use the information provided and convert the units accordingly. Here are the steps to solve this problem:
Step 1: Convert the rate from miles per hour to feet per hour.
Since the diameter of the wheels is given in feet, we need to work with the same unit of measurement. There are 5,280 feet in a mile, so we can convert the rate by multiplying it by 5,280.
65 miles/hour * 5,280 feet/mile = 343,200 feet/hour
Step 2: Calculate the distance traveled by the car in one minute.
To find the distance traveled in one minute, we need to divide the distance per hour by 60 since there are 60 minutes in an hour.
343,200 feet/hour ÷ 60 minutes/hour = 5,720 feet/minute
Step 3: Calculate the circumference of the wheels.
The circumference of a circle can be calculated using the formula: Circumference = π * diameter. Given that the diameter of the wheels is 2.5 feet, we can find the circumference by multiplying it by π (approximately 3.14159).
Circumference = 3.14159 * 2.5 feet = 7.85475 feet
Step 4: Calculate the number of revolutions per minute.
We can find the number of revolutions per minute by dividing the distance traveled in one minute by the circumference of the wheels.
Number of revolutions per minute = Distance traveled in one minute ÷ Circumference of the wheels
Number of revolutions per minute = 5,720 feet/minute ÷ 7.85475 feet = 729.265
Therefore, the wheels of the car are rotating approximately 729.265 revolutions per minute.
First convert miles per hour to feet per second.
65 mph = 95.3 ft/s
The rotation rate of the wheels in radians per second, w, is
w = (speed)/(radius) = (95.3 ft/s)/(1.25 ft)
= 76.3 radians/s
Convert that to rpm by multiplying by
(60 s/min)*[1/(2 pi)] rev/rad)
729 rpm