$3.[25$ points$]$ Figure below shows a cross section of an automatic brake fitted to a rotating shaft. The brake pads are held on the shaft bv snrings.

a$.$ Explain why the brake pads press against the inner surface of the stationary collar if the shaft rotates too fast.

b$.$ Each brake pad and its retainer has a mass of $0\mathrm{.}30$ kg and its centre of mass is $60$ mm from the centre of the shaft. The tension in the spring attached to each pad is $250$ N $.$ Calculate the maximum frequency of rotation of the shaft for no braking.

c$.$ Automatic brakes of the type described above are used on ships to prevent lifeboats falling freely when they are lowered on cables onto the water. Discuss how the performance of the brake would be affected if the springs gradually became weaker with time.