Question 174: Centre of Mass and Rotational Motion

Question

The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m
2
.

Accepted Answer

Parallel axis theorem
I = I
CM
+ Md
2
$$I = {{M{r^2}} \over 2} + M{\left( {{L \over 2}} ight)^2}$$
$$2.7 = M{{{{(0.2)}^2}} \over 2} + M{\left( {{{0.8} \over 2}} ight)^2}$$
$$2.7 = M\left[ {{2 \over {100}} + {{16} \over {100}}} ight]$$
M = 15 kg
$$ \Rightarrow ho  = {M \over {\pi {r^2}L}} = {{15} \over {\pi {{(0.2)}^2} 	imes 0.8}}$$
= 0.1492 $$	imes$$ 10
3

Answer

14.9 kg/m
3

Answer

7.5 $$	imes$$ 10
1
kg/m
3

Answer

7.5 $$	imes$$ 10
2
kg/m
3

Answer

1.49 $$	imes$$ 10
2
kg/m
3

Centre of Mass and Rotational Motion

The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m 2 .

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