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A spot of paint on a bicycle tire moves in a circular path of radius 0.29 m. when the spot has traveled a linear distance of 1.31 m, through what angle has the tire rotated? give your answer in radians.

Respuesta :

skyluke89
First we need to calculate the perimeter of the tire. Given the radius, r=0.29 m, the perimeter is
[tex]p= 2 \pi r = 2 \pi (0.29 m)=1.82 m[/tex]
This is the length of one complete revolution, and the angle that corresponds to this distance is [tex]2 \pi rad[/tex]. So, if we want to find what is the angle that corresponds to a distance of 1.31 m, we can set a simple proportion:
[tex]1.82 m : 2 \pi rad = 1.31 m : x[/tex]
From which we find x, the angle through which the tire has rotated:
[tex]x= \frac{1.31 m \cdot 2 \pi rad}{1.82 m}=4.52 rad [/tex]
raphealnwobi

The tire rotated an angle of 4.5 rad to travel a linear distance of 1.31 m

What is a circle?

A circle is the locus of a point such that its distance from a fixed point known as the center is always constant.

The radius of the bicycle wheel is 0.29 m, hence:

Circumference of bicycle tire = 2π * radius = 2π(0.29) = 1.82 m

For traveling a distance of 1.31 m:

1.31 = angle in rads * radius

Angle * 0.29 = 1.31

Angle = 4.5 rad

The tire rotated an angle of 4.5 rad to travel a linear distance of 1.31 m

Find out more on circle at: https://brainly.com/question/22965557

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