(Solved): 2. A wheel of radius \( 20 \mathrm{~cm} \) has a constant angular acceleration of \( \alpha=0.5 \m ...

2. A wheel of radius \( 20 \mathrm{~cm} \) has a constant angular acceleration of \( \alpha=0.5 \mathrm{rad} / \mathrm{s}^{2} \) starting from rest. After it turns through an angle of \( 100 \mathrm{rad} \), calculate: (a) the angular velocity \( \vec{\omega} \) of the wheel; (b) the time elapsed after the wheels starts turning; (c) the velocity \( \vec{v} \) and acceleration \( \vec{a} \) of a ladybug on the edge of the wheel. Express answers in (a) and (c) as vectors using the coordinate system \( \hat{\mathbf{r}}, \hat{\mathbf{t}} \), and \( \hat{\mathrm{k}} \) as shown in the figure.