Steel Rotary

Any help you can give me on the following question?

(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

In (a) you state, ‘without slipping or sliding’.

There must be rolling friction to overcome and obviously the weight of the roller will cause a compression of the surface it is on.

Consequently some energy is required to ‘climb’ out of the depression it makes irrespective of the depth.

Unless you can supply the ‘rolling frictional resistance’ the remainder of the question is pointless.

in (b) you quote a frictional force of 145N to bring the roller to a stop. This seems to be a ridiculously small force, given the mass of the roller and its total kinetic energy.

In addition the ANGLE of the slope will influence the LENGTH it has to travel in falling through 0.6m and obviously the FRICTIONAL RESISTANCE will depend upon the angle of the slope.

Imagine if the slope is either almost (1) horizontal (2) vertical. Will frictional resistance remain constant, given the mass of the roller?

The question is flawed!

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