You are designing a clutch assembly which consists of two

Chapter 2, Problem 83GP

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You are designing a clutch assembly which consists of two cylindrical plates, of mass \(M_{\mathrm{A}}=6.0 \mathrm{~kg}\) and \(M_{\mathrm{B}}=9.0 \mathrm{~kg}\), with equal radii \(R=0.60 \mathrm{~m}\). They are initially separated (Fig. 8-57). Plate \(M_{\mathrm{A}}\) is accelerated from rest to an angular velocity \(\omega_1=7.2 \mathrm{rad} / \mathrm{s}\) in time \(\Delta t=2.0 \mathrm{~s}\). Calculate

(a) the angular momentum of \(M_{\mathrm{A}}\), and

(b) the torque required to have accelerated \(M_{\mathrm{A}}\) from rest to \(\omega_1\).

(c) Plate \(M_{\mathrm{B}}\), initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate \(M_{\mathrm{A}}\) (their contact surfaces are high-friction). Before contact, \(M_{\mathrm{A}}\) was rotating at constant \(\omega_1\). After contact, at what constant angular velocity \(\omega_2\) do the two plates rotate?

                                                                 

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