We are given the time for an object to complete 20 revolutions in a circular path. To determine the velocity of the object we need to use the following formula:
[tex]v=\frac{S}{T}[/tex]
Where:
[tex]\begin{gathered} v=\text{ velocity} \\ S=\text{ lenght of the circular path (circumpherence)} \\ T=\text{ period} \end{gathered}[/tex]
To determine the value of "S" we use the following:
[tex]S=2\pi r[/tex]
Where:
[tex]r=\text{ radius}[/tex]
Now, we substitute in the formula for the velocity:
[tex]v=\frac{2\pi r}{T}[/tex]
To determine the period we need to divide the time to complete the 20 revolutions by the number of revolutions, like this:
[tex]T=\frac{t}{20}[/tex]
For example, let's take the first value and plug it into the formula:
[tex]T=\frac{24.09s}{20\text{rev}}=1.2s[/tex]
Now, we plug in the value of the radius and the period in the formula for the speed and we get:
[tex]v=\frac{2\pi(0.22m)}{1.2s}[/tex]
Solving the operations:
[tex]v=1.15\frac{m}{s}[/tex]
Therefore, the velocity of the bob is 1.15 m/s.
