You have a pulley 14.6 cm in diameter and with a mass of 1.7 kg. You get to wond

Question

You have a pulley 14.6 cm in diameter and with a mass of 1.7 kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is it concentrated toward the center or the rim? To find out, you hang the pulley on a hook, wrap a string around it several times, and suspend your 1.5 kg physics book 1.5 m above the floor. With your stopwatch, you can find that it takes 0.60 s for your book to hit the floor.

What is the moment of inertia if the pulley is uniform? 0.00453 kg m2

What is the actual moment of inertia of the pulley based on your measurement? ______ kg m2

Explanation / Answer

a) we know
I=.5*m*r^2 =0.00453 kg m2

b) 1.5=.5*a*0.60^2
solve for a
a=3/0.6^2 = 8.33 m-sec^-2

then
Tension in the string during the fall
T*r=I*a/r where I is the moment of the pulley

and
T=1.5*(g-a) of the book
combine

I=r^2*1.5*(g-a)*/a =1.4* 10^-3 kg m2

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