Question

The axis of rotation of a thin plate is located at the left side, as shown in the figure.

A rectangle with a base labeled uppercase L and a height labeled lowercase w. A vertical, dashed line runs along the leftside of the rectangle's height. A circular arrow around the vertical, dashed line indictates that the rectangle rotates about its left edge.

Calculate the moment of inertia
if the plate has a length of 9.00 cm, a width of 7.00 cm, and a uniform mass density of 1.50 g/cm2.

Answer 1

The moment of inertia of the rectangular plate is  $1.02 \times 10^{-4} \ kg.m^2$.

The given parameters;

• length of the rectangle, a = 9 cm
• width of the rectangle, b = 7 cm
• mass density of rectangle, = 1.5 g/cm²

The area of the rectangular plate is calculated as;

A = ab

A = 9 cm x 7 cm = 63 cm²

The mass of the rectangular plate is calculated as;

m = 1.5 g/cm²  x  63 cm²

m = 94.5 g

m = 0.0945 kg

The moment of inertia of the rectangular plate is calculated as follows;

$I = \frac{m}{12}(a^2 + b^2)\\\\I = \frac{0.0945(0.09^2 \ + \ 0.07^2)}{12} \\\\I =\frac{0.0945(0.013)}{12} \\\\I = 1.02 \times 10^{-4} \ kg.m^2$

Thus, the moment of inertia of the rectangular plate is  $1.02 \times 10^{-4} \ kg.m^2$.

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