Question

A rock tied to the end of string swings at a constant angular rate. If you are told thatthe string can support a total of 210 N of force before breaking, what is the maximumangular velocity the rock can rotate if the rock has a mass of 0.23 kg, and the length ofthe string is 0.35 m? Give your answer in units of radian per second.

Answer 1

Given data

The magnitude of the total force is F = 210 N

The mass of the rock is m = 0.23 kg

The length of the string is L = 0.35 m

The expression for the maximum angualr velocity is given as:

`\begin{gathered} F=m\omega^2L \\ \omega=\sqrt{(F)/(mL)} \end{gathered}`

Substitute the value in the above equation.

`\begin{gathered} \omega=\sqrt[]{\frac{210\text{ N}}{0.23\text{ kg }*\text{0.35 m}}} \\ \omega=51.07\text{ rad/s} \end{gathered}`

Thus, the maximum angular velocity of the rock is 51.07 rad/s.