A bicycle wheel of diameter 26 inches is rolled through an angle of 720 degrees. how far has the wheel moved?
Diameter =26"
radius,r = 26"/2 = 13"
Angle = 2πr / turn
Distance = circumference for 2 turns
=2*2πr
=4πr
52
To calculate how far the bicycle wheel has moved, we need to determine the distance covered by one complete revolution of the wheel. This can be calculated using the circumference formula:
Circumference = π * diameter
Given that the diameter of the wheel is 26 inches, we can substitute this value into the formula and solve for the circumference:
Circumference = π * 26 inches
Now, we need to find out how many revolutions the bicycle wheel has made based on the angle it has rolled. One complete revolution equals 360 degrees.
Revolutions = Angle / 360
In this case, the given angle is 720 degrees, so we can calculate the number of revolutions as follows:
Revolutions = 720 degrees / 360 degrees = 2 revolutions
To find out how far the wheel has moved, we multiply the calculated circumference by the number of revolutions:
Distance moved = Circumference * Revolutions
Substituting in the values we calculated earlier:
Distance moved = (π * 26 inches) * 2 revolutions
Now, we can calculate the numerical value of the distance moved:
Distance moved ≈ 81.64 inches (rounded to two decimal places)
Therefore, the bicycle wheel has moved approximately 81.64 inches.
To find how far the wheel has moved, we need to calculate the distance covered by one complete revolution of the wheel.
The formula to calculate the circumference (C) of a circle is:
C = π * d
where d is the diameter of the circle.
In this case, the diameter of the bicycle wheel is given as 26 inches. Using this, we can find the circumference:
C = π * 26 inches
Since the problem states that the wheel is rolled through an angle of 720 degrees (which is equivalent to two complete revolutions), the distance covered by the wheel would be twice the circumference.
So, to find how far the wheel has moved, we multiply the circumference by 2:
Distance covered = 2 * C
To get the numerical value, we can use the approximate value of π as 3.14:
Distance covered = 2 * 3.14 * 26 inches
Now, you can calculate the distance covered by multiplying the values:
Distance covered = 2 * 3.14 * 26 inches = 163.84 inches
Therefore, the wheel has moved approximately 163.84 inches.