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(a) A heavy industrial mill roller gets loose and rolls down a slope without slipping or sliding. It drops in height 900 mm. it is made of steel and is a hollow cylinder of outer diameter 600 mm, inner diameter 400 mm and length 1.2 m. assuming the density of steel is 7860 kg m-3, determine:

(i) the mass of the roller

(ii) the second moment of mass of the roller

(iii) the energy of the roller at the bottom of the slope

(iv) the speed of the roller at the bottom of the slope

(b) Once on the horizontal floor, the roller slows to a stop. The total frictional force required to bring the roller to a stop is calculated as 145 N.

Calculate, assuming again that the roller doesn’t slide or slip and that the frictional force required to decelerate rotary motion is Iα/r²:

(i) the shortest distance that the roller will cover before stopping

(ii) the time taken for the roller to stop

Thank you