A clutch assembly consists of two cylindrical plates, MA = 7.0 kg and MB with an

Question

A clutch assembly consists of two cylindrical plates, MA = 7.0 kg and MB with an unknown mass. Both plates have the same radii R = 0.6 m. They are initially separated. Plate MA is accelerated from rest to an angular velocity ?1 = 6.4 rad/s in time dt by a torque of 6.6 N·m.
(a) Calculate the moment of the inertia of MA kg·m2
(b) Calculate the acceleration time dt. s
(c) Plate MB, initially at rest and free to rotate without friction, is allowed to fall vertically so it is in firm contact with plate MA. Before contact, MA was rotating at constant ?1. After contact, the two plates rotate at a constant angular velocity ?2 = 2.6 rad/s. What is the mass of MB? kg

Explanation / Answer

a) Ia = mar2 /2   = 7 x 0.62 /2 = 1.26 kg-m2

b) = I

= 6.6 / 1.26 = 5.24 rad/s2

t = 6.4 / 5.24 = 1.223 sec

c) using angular momentum conservation,(I)

1.26 x 6.4 + 0 = (Ib + 1.26) x 2.6

(Ib + 1.26) = 3.11

Ib = mb X 0.62 /2    = 3.11 - 1.26 = 1.84

mb = 10.23 kg

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