Question

A meter stick is rotated about the end labeled 0.00 cm, so that the other end of the stick moves through an arc length of 8.85 cm. Through what arc length s does the 25.0-cm mark on the stick move?

Answer 1

Answer:

2.215 cm

Explanation:

length of stick (L) = 1 m

length of arc by the 1 m stick (La) = 8.85 cm = 0.885 m

Through what arc length does the 25.0-cm (0.25 m) mark on the stick move?

from the attached diagram:

OA = length of the stick = 1 m

OC = mark on stick = 0.25 m

AB = length of arc by the full stick length = 0.885 m

CD = length of arc by the 25 cm mark =?

length of an arc = radius x θ  (θ is the angle and radius is the length of the stick in this case)

therefore

AB = OA x θ

θ = AB / OA = 0.0885 / 1 = 0.885 rad

also

CD = OC X θ

CD = 0.25 X 0.0885 =0.02215 m = 2.215 cm

Answer 2

The arc length moved by 25 cm mark on the stick is 2.2 cm.

The given parameters;

when the length of meter rule is 1 m, arc length = 8.85 cm

The angular distance made by the arc is calculated as follows;

2πrN = 0.0885

$N = \frac{0.0885}{2\pi \times 1} \\\\N = 0.014 \ rev\\\\N = 0.014 \times 2\pi = 0.088 \ rad$

The arc length when the mark is 25 cm

D = 0.088 x 0.25

D = 0.022 m

D = 2.2 cm

Thus, the arc length moved by 25 cm mark on the stick is 2.2 cm.

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