A uniform wooden meter stick has a mass of m = 795 g. A clamp can be attached to

Question

A uniform wooden meter stick has a mass of m = 795 g. A clamp can be attached to the measuring stick at any point so that it can freely pivot around point P, which is a distance d from the zero-end of the stick as shown. Part (a) Calculate the moment of inertia in kgm2 of the meter stick if the pivot point P is at the 50-cm mark. Part (b) Calculate the moment of inertia in kgm2 of the meter stick if the pivot point P is at the 0-cm mark d = 0 cm. Part (c) Calculate the moment of inertia in kgm2 of the meter stick if the pivot point P is at the d = 25 cm mark. Part (d) Calculate the moment of inertia in kgm2 of the meter stick if the pivot point P is at the d = 55 cm mark. Part (e) Determine a general expression for the moment of inertia of a meter stick Ie of mass m in kilograms pivoted about point P, any distance d in meters from the zero-cm mark. Part (f) The meter stick is now replaced with a uniform yard stick with the same mass of m = 795 g . Calculate the moment of inertia in kgm2of the yard stick if the pivot point P is at the 50-cm mark.

Explanation / Answer

moment of inertia about mid point = mL2/12 = 0.06625

moment of inertia about end point = mL2/3 = 0.265

using parallel axis theorem -

I = Icm + md2

I = 0.06625 + 0.795*0.25*0.25

I = 0.1159 Kg-m2

here d = distance of the point from centre of mass where CM will be middle of the stick

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