Answer:
[tex]v=0.57\frac{m}{s}[/tex]
[tex]a_c=10.83\frac{m}{s^2}[/tex]
Explanation:
We have an uniform circular motion, therefore, the pebble’s speed is given by the distance traveled in a revolution [tex](2\pi r)[/tex] and the period (T), since this is the time pebble’s takes to complete a revolution:
[tex]v=\frac{2\pi r}{T}[/tex]
The period is inversely proportional to the frequency:
[tex]T=\frac{1}{f}[/tex]
So, we have:
[tex]v=\frac{2\pi r}{\frac{1}{f}}\\v=2\pi rf\\[/tex]
Recall that the radius is the half of the diameter and one revolution per is equal to one Hz:
[tex]v=2\pi (30*10^{-2}m)(3Hz)\\v=0.57\frac{m}{s}[/tex]
The centripetal acceleration is defined as:
[tex]a_c=\frac{v^2}{r}\\a_c=\frac{(0.57\frac{m}{s})^2}{30*10^{-2}m}\\\\a_c=10.83\frac{m}{s^2}[/tex]
