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Chapter 1: Q13DQ (page 294)

Describe how you could use part (b) of Table 9.2 to derive the result in part (d)

Short Answer

Expert verified

The expressionl=13Ma2is derived.

Step by step solution

01

Concept/Significance of Moment of inertia of Slender rod, axis through one end

The moment of inertia of the slender rod with mass M and length L and axis through one end is given by,

Irod=13ML2

02

Derive the result 13Ma2

Consider the rectangular plate as shown below.

It can be seen that the moment of inertial of the rectangular plate about the axis is lplane. The moment of inertia of a rod with thickness dx and length a is given by,

dI=13(dm)a2鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�......(1)

Find dm as follows.

dmM=dxbdm=Mbdx

From equation (1),

dI=13Mbdxa2

Integrate the above equation.

鈭�dl=鈭�0b13Mbdxa2l=13Mba2x0b=13Mba2b=13Ma2

Therefore, the expression l=13Ma2is derived.

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