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 8.60 cm. Through what arc length s does the 25.0-cm mark on the stick move?
I have no clue what Im doing, I know S=tr but what is t?
To find the arc length through which the 25.0-cm mark on the stick moves, we can use the formula:
s = θr
Where:
- s is the arc length
- θ is the angle in radians
- r is the radius or distance from the center of rotation
In this case, the angle θ is not given directly. However, we can determine it by comparing the distances of the 25.0-cm mark and the end labeled 0.00 cm from the center of rotation.
The distance of the 25.0-cm mark from the center of rotation is 25.0 cm, which corresponds to an arc length of 8.60 cm. Let's call this angle θ₁.
Similarly, the distance of the end labeled 0.00 cm from the center of rotation is 0 cm, which corresponds to an arc length of 0 cm. Let's call this angle θ₂.
Since angles measured in radians are directly proportional to the ratio of arc lengths to radii, we can set up the following proportion:
θ₁ / θ₂ = s₁ / s₂
Where:
- θ₁ is the angle through which the 25.0-cm mark moves
- θ₂ is the angle through which the end labeled 0.00 cm moves
- s₁ is the given arc length of 8.60 cm
- s₂ is the desired arc length (unknown)
We know that θ₂ is 0 radians, so we can rewrite the proportion as:
θ₁ / 0 = s₁ / s₂
This simplifies to:
θ₁ * s₂ = 0 * s₁
θ₁ * s₂ = 0
Since anything multiplied by 0 is 0, we conclude that θ₁ * s₂ = 0. This implies that s₂ = 0.
Therefore, the arc length through which the 25.0-cm mark on the stick moves is 0 cm.