Compared to the number of radians in one revolution of a bicycle tire with a radius of 33 centimeters, the number of radians in one revolution of a go-cart wheel (radius = 22 centimeters) is:
the same
To compare the number of radians in one revolution of the bicycle tire and the go-cart wheel, we need to calculate the circumference of each wheel.
The formula to calculate the circumference of a circle is:
Circumference = 2 * π * radius
For the bicycle tire:
Radius = 33 centimeters
Circumference of the bicycle tire = 2 * π * 33 centimeters
For the go-cart wheel:
Radius = 22 centimeters
Circumference of the go-cart wheel = 2 * π * 22 centimeters
Now that we have the circumferences of both wheels, we can calculate the number of revolutions in one revolution of each wheel.
The formula to calculate the number of revolutions is:
Number of revolutions = Circumference / Circumference of one revolution
Since we want to find the number of radians in one revolution, we know that one revolution of a circle is equal to 2π radians. Therefore, the number of radians in one revolution of each wheel is equal to the number of revolutions multiplied by 2π.
Let's calculate the number of radians in one revolution of each wheel:
For the bicycle tire:
Number of revolutions = Circumference of the bicycle tire / Circumference of one revolution of the bicycle tire
Number of radians in one revolution of the bicycle tire = Number of revolutions * 2π
For the go-cart wheel:
Number of revolutions = Circumference of the go-cart wheel / Circumference of one revolution of the go-cart wheel
Number of radians in one revolution of the go-cart wheel = Number of revolutions * 2π
Now, let's plug in the values and calculate:
For the bicycle tire:
Circumference of the bicycle tire = 2 * π * 33 centimeters
Number of revolutions of the bicycle tire = (2π * 33) / (2π) = 33
Number of radians in one revolution of the bicycle tire = 33 * 2π
For the go-cart wheel:
Circumference of the go-cart wheel = 2 * π * 22 centimeters
Number of revolutions of the go-cart wheel = (2π * 22) / (2π) = 22
Number of radians in one revolution of the go-cart wheel = 22 * 2π
Therefore, compared to the number of radians in one revolution of a bicycle tire with a radius of 33 centimeters, the number of radians in one revolution of a go-cart wheel with a radius of 22 centimeters is 22 * 2π.