A simple model of a clutch assembly for a motorbike consists of two coaxial circular discs, X and Y, each of radius 12.0 cm. Both discs can rotate without friction. Disc X, of mass 2.5 kg, is made to rotate, from rest, to 3 revolutions s−1 by a torque, τ, in a time of 1.5 s. (I=21MR2 for a disc.)
a. a Calculate the angular momentum gained by disc X.
b. b Hence, calculate the torque, τ, required to accelerate the disc.
c. c When a gear is engaged, disc Y, of mass 4.5 kg, which had previously been at rest, is pushed against disc X so that the two discs stick together due to the friction between the disc faces. Calculate the new number of revolutions that the two-disc system makes per second.