Answer
(a) $1.4$ rad/s (b) $v_1=2.8m/s$, $v_2=2.1m/s$
Work Step by Step
(a) To find the angular speed, use the formula $$\omega=\frac{\Delta \theta}{\Delta t}$$ Substituting known values of $\Delta \theta=2\pi rad$ (one full revolution) and $\Delta t=4.5s$ yields an angular speed of $$\omega=\frac{2\pi rad}{4.5s}=1.4rad/s$$ (b) The linear speed of a point on a rotating body is equal to $v=r\omega$. For child 1, this value is equal to $$v_1=r_1\omega=(2.0m)(1.4rad/s)=2.8m/s$$ For child 2, this value is $$v_2=r_2\omega=(1.5m)(1.4rad/s)=2.1m/s$$
