A spot of paint on a bicycle tire moves in a circular path of radius 0.27 m. When the spot has traveled a linear distance of 2.18 m, through what angle has the tire rotated? Give your answer in radians.
To determine the angle through which the tire has rotated, we can use the formula:
θ = s / r
where θ is the angle in radians, s is the linear distance traveled by the spot of paint, and r is the radius of the circular path.
Substituting the given values into the formula:
θ = 2.18 m / 0.27 m
Simplifying the division:
θ = 8.0741
Therefore, the tire has rotated through an angle of approximately 8.0741 radians.
To find the angle through which the tire has rotated, we can use the formula:
θ = s / r
Where:
θ is the angle
s is the linear distance traveled by the spot of paint
r is the radius of the circular path
In this case, the linear distance traveled by the spot of paint is given as 2.18 m, and the radius of the circular path is 0.27 m.
Plugging these values into the formula, we have:
θ = 2.18 m / 0.27 m
Calculating this division, we find:
θ ≈ 8.07
Therefore, the tire has rotated approximately 8.07 radians.
angleinradians* radius= arcdistance
angleinradians= 2.18/r