A bicycle with 26 inch diameter wheels is traveling at 10mph, to the nearest whole number how may revolutions does each wheel make per minute?
A bicycle with 28-in.-diameter wheel is traveling at 15 mph. To the nearest whole number, how many revolutions does each wheel make per minute?
Answer: About 129 Revolutions per minute
Formula: Revolution/minute=Velocity/circumference of circle
Convert 10 miles/hr to inches per minutes
substitute that into the formula and solve. done!
To find the number of revolutions each wheel makes per minute, we need to calculate the distance traveled by the bicycle in one revolution.
The formula to calculate the distance traveled in one revolution is:
Distance = π × diameter
Given that the diameter of the wheel is 26 inches, we can calculate its radius by dividing the diameter by 2:
Radius = diameter / 2 = 26 / 2 = 13 inches
Now, let's calculate the distance traveled in one revolution using the formula:
Distance = π × 13 inches
Considering π (pi) as approximately 3.14, we can calculate the distance:
Distance ≈ 3.14 × 13 inches
Calculating the value:
Distance ≈ 40.82 inches
Since the bicycle is traveling at 10 mph, we need to convert the speed into inches per minute:
10 mph = 10 × 5280 feet per hour
10 × 5280 feet per hour = 52800 feet per hour
52800 feet per hour = 633600 inches per hour
633600 inches per hour = 633600 ÷ 60 inches per minute
633600 ÷ 60 inches per minute ≈ 10560 inches per minute
Now we can find the number of revolutions per minute by dividing the speed in inches per minute by the distance traveled in one revolution:
Revolutions per minute = Speed / Distance
Revolutions per minute ≈ 10560 inches per minute ÷ 40.82 inches
Revolutions per minute ≈ 259 revolutions per minute (rounded to the nearest whole number)
Therefore, each wheel makes approximately 259 revolutions per minute.
To find the number of revolutions each wheel makes per minute, we need to calculate the distance traveled by the bicycle in one minute and then divide it by the circumference of the wheel.
First, let's find the circumference of the wheel. The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius of the circle.
Given that the diameter of the wheel is 26 inches, the radius will be half of that, which is 13 inches. Therefore, the circumference of the wheel is C = 2π(13) = 26π inches.
Next, to find the distance traveled in one minute, we need to convert the speed of the bicycle from miles per hour to inches per minute. Since 1 mile is equal to 5,280 inches (5280 ft / mile * 12 in/ft), we can multiply the speed by this conversion factor:
Distance in inches per minute = Speed in mph * 5280 inches/mile / 60 minutes/hour
= 10 mph * 5280 inches/mile / 60 minutes/hour
≈ 880 inches per minute
Finally, to find the number of revolutions each wheel makes per minute, we divide the distance traveled in one minute by the circumference of the wheel:
Number of revolutions per minute = Distance traveled in one minute / Circumference of the wheel
= 880 inches per minute / (26π inches)
≈ 10.63 revolutions per minute
Rounding to the nearest whole number, each wheel makes approximately 11 revolutions per minute.