To determine the velocity of the platter, we need to follow these steps:
1. Calculate the circumference of the platter:
The circumference [tex]\(C\)[/tex] of a circle is calculated using the formula:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\(r\)[/tex] is the radius of the circle.
Given that the radius of the platter is [tex]\(12.9 \text{ cm}\)[/tex], we get:
[tex]\[
C = 2 \pi \times 12.9 \text{ cm}
\][/tex]
This yields a circumference of:
[tex]\[
C \approx 81.05 \text{ cm}
\][/tex]
2. Determine the velocity:
The velocity [tex]\(v\)[/tex] of an object moving along a circular path is given by the formula:
[tex]\[
v = \frac{C}{T}
\][/tex]
where [tex]\(T\)[/tex] is the period of rotation.
With a period [tex]\(T\)[/tex] of [tex]\(4.71 \text{ seconds}\)[/tex], and the previously calculated circumference:
[tex]\[
v = \frac{81.05 \text{ cm}}{4.71 \text{ s}}
\][/tex]
This gives a velocity of:
[tex]\[
v \approx 17.21 \text{ cm/s}
\][/tex]
Therefore, the velocity of the platter is:
[tex]\[
v \approx 17.21 \text{ cm/s}
\][/tex]
