1. If a bicycle wheel has a diameter of 27 inches, find the radian measure of the angle through which the wheel turns as the bicycle travels a distance of one mile.
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A bicycle tire has a diameter of 1.4 meter how many meter does the bicycle move when the tire turn one revolution
Where is k2.
To find the radian measure of the angle through which the wheel turns as the bicycle travels one mile, we need to determine how many revolutions the wheel makes.
First, let's find the circumference of the wheel. The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
Since the diameter is given as 27 inches, we can find the radius by dividing the diameter by 2:
Radius = 27 inches / 2 = 13.5 inches
Now, let's calculate the circumference:
Circumference = 2 * π * 13.5 inches
Next, we need to convert the distance traveled from miles to inches. There are 5,280 feet in one mile and 12 inches in one foot, so one mile is equal to:
One mile = 5,280 feet * 12 inches/foot = 63,360 inches
To find the number of revolutions the wheel makes, we divide the distance traveled by the circumference of the wheel:
Number of revolutions = Distance traveled / Circumference
Number of revolutions = 63,360 inches / (2 * π * 13.5 inches)
Now, we can find the radian measure of the angle by multiplying the number of revolutions by 2π (since one revolution is equal to 2π radians):
Radian measure = Number of revolutions * 2π
Radian measure = (63,360 inches / (2 * π * 13.5 inches)) * 2π
Simplifying, we cancel out the inches and π:
Radian measure = (63,360 / 27) * 2
Radian measure = 234.67 radians (approximately)
Therefore, the radian measure of the angle through which the wheel turns as the bicycle travels one mile is approximately 234.67 radians.
To find the radian measure of the angle through which the wheel turns as the bicycle travels a distance of one mile, we need to first find the circumference of the wheel.
The circumference of a circle can be calculated using the formula:
C = 2πr
Given that the diameter of the wheel is 27 inches, we can determine the radius by dividing the diameter by 2:
r = 27 inches / 2 = 13.5 inches
Now, we can calculate the circumference of the wheel:
C = 2π(13.5 inches)
C ≈ 84.78 inches
Since we want to find the angle turned as the bicycle travels one mile, we need to convert the distance to inches. There are 5,280 feet in a mile, and since there are 12 inches in a foot, we have:
1 mile = 5,280 feet * 12 inches/foot = 63,360 inches
Now we can find the radian measure using the formula:
angle (in radians) = distance / circumference
angle (in radians) = 63,360 inches / 84.78 inches
angle (in radians) ≈ 746.51 radians
Therefore, the radian measure of the angle through which the wheel turns as the bicycle travels one mile is approximately 746.51 radians.