A dart of inertia \(m_{\mathrm{d}}\) is fired such that it strikes with speed \(v_{\mathrm{d}}\), embedding its tip in the rim of a target that is a uniform disk of inertia \(m_{\mathrm{t}}\) and radius \(R_{\mathrm{t}}\). The target is initially rotating clockwise in the view shown in Figure P11.90, with rotational speed \(\omega\) about an axis that runs through its center and is perpendicular to its plane. Assume that the dart's inertia is concentrated at its tip. What is the final rotational speed of the target if the dart strikes

(a) tangent to the target rim as in Figure P11.90a and \((b)\) normal to the rim as in Figure P11.90b?

Data from Figure P11.90

Transcribed Image Text:

(a) R ma (b) m 3 R ma