Answer
See the detailed answer below.
Work Step by Step
We are given this equation;
$$60\;\rm N=(0.3\;kg)\omega^2(0.5\;m)$$
We can see that the 60 N is representing a radial force exerted on a 0.3 kg object which is moving in a circular path of radius 0.5 m.
a) A boy is attaching a 0.3-kg rock to a wire and rotating it in a horizontal plane at which the radial force exerted on it is constant and equal to 60 N. The radius of the circular path is 50 cm, find its angular speed.
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b) Solving the given formula for $\omega$
$$\omega=\sqrt{\dfrac{60}{0.5\times 0.3}}$$
$$\omega=\color{red}{\bf 20}\;\rm rad/s$$
