Calculate the moment of inertia in kg middot nr of the meter stick if the pivot

Question

Calculate the moment of inertia in kg middot nr of the meter stick if the pivot point P is at the 50-cm mark. Calculate the moment of inertia in kg middot nr of the meter stick if the pivot point Pis at the 0-cm mark d = 0 cm. Calculate the moment of inertia in kg middot nr of the meter stick if the pivot point P is at the d = 25 cm mart Calculate the moment of inertia in kg middot m^2 of the meter stick if the pivot point P is at the d = 63 cm mark. Determine a general expression for the moment of inertia of a meter stick/, of mass m in kilograms pivoted about point P. any distance d in meters from the zero-cm mark The meter stick is now replaced with a uniform yard stick with the same mass of m = 749 g. Calculate the moment of inertia in kg middot m^2 of the yard stick if the pivot point P is at the 50-cm mark.

Explanation / Answer

a )   

mL^ /12 = 0.749 *1^2 /12 =0.0624166667 kg .m^2

b)

mL^ / 3    0.749 *1^2 /3   0.249666667  kg .m^2

c)

I = Icm + mr^2 = mL^ /12 + m*( 0.25) ^2 = 0.749 *1^2 /12 + 0.749 * 0.25^2 =0.109229167 kg .m^2

d)

I = Icm + mr^2 = mL^ /12 + m*( 0.50- 0.63) ^2 = 0.749 *1^2 /12 + 0.749 * 0.13^2 = 0.0750747667 kg.m^2

e)

genral expression   

I =  mL^ /12 + m ( 0.50 - d)^2

f)

yard stick length L =0.9144 m

CG of yard stick = 0.9144 /2 =0.4572

so

I = mL^ /12 + m ( 0.4572 - d)^2 = 0.749 *0.9144^2/ 12 + 0.749 *(  0.4572 - 0.50)^2 =0.0535603309 kg.m^2

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