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 6.20 cm. Through what arc length s does the 25.0-cm mark on the stick move?
any help, please?
s = rθ
solve for θ and then use the same eq with the new radius.
To find the arc length that the 25.0-cm mark on the stick moves, we can use the concept of proportionality.
Let's assume that the meter stick consists of 100 equal divisions (from 0 cm to 100 cm). In this case, each division would be equal to 1 cm.
Now, we know that the other end of the stick moves through an arc length of 6.20 cm, which corresponds to 100 divisions.
To calculate the arc length for the 25.0-cm mark, we need to determine how many divisions it represents. We can set up a proportion:
100 divisions corresponds to 6.20 cm
x divisions (the 25.0-cm mark) corresponds to s cm (the arc length we want to find)
Using the proportion formula:
100/6.20 = x/s
Now, we can rearrange the equation to solve for s:
s = (6.20 * x) / 100
Since we want to find the arc length s for the 25.0-cm mark, we substitute x = 25.0 into the equation:
s = (6.20 * 25.0) / 100
s = 1.55 cm
Therefore, the 25.0-cm mark on the stick moves through an arc length of 1.55 cm.