You have a pulley 10.1 cm in diameter and with a mass of 2.5 kg. You get to wond

Question

You have a pulley 10.1 cm in diameter and with a mass of 2.5 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 1.9 kg physics book 1.4 m above the floor. With your stopwatch, you can find that it takes 0.58 s for your book to hit the floor.

What is the moment of inertia if the pulley is uniform?

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

What do you conclude about the pulley?

The pulley is uniform (within 1% of uniform)The mass of the pulley is concentrated toward the center    The mass of the pulley is concentrated toward the rim

Explanation / Answer

radius of the pulley, r = d/2

= 0.101/2

= 0.0505 m

If the pulley is uniform,

I = 0.5*M*r^2

= 0.5*2.5*0.0505^2

= 3.188*10^-3 kg.m^2 <<<<<----------Answer

let a is the acceleration of the physics book.

now Apply, h = u*t + 0.5*a*t^2

h = 0.5*a*t^2 (since initial velocity, u = 0)

a = 2*h/t^2

= 2*1.4/0.58^2

= 8.32 m/s^2

so, tension in the string.

T = m*g - m*a

= 1.9*9.8 - 1.9*8.32

= 2.812 N

r = d/2

= 0.101/2

= 0.0505 m

angular acceration of pulley, alfa = a/r

= 8.32/0.0505

= 164.75 rad/s^2

now Apply, net torque = I*alfa

T*r = I*alfa

I = T*r/alfa

= 2.812*0.0505/164.75

= 8.62*10^-4 kg.m^2 <<<<<<<----------Answer (actual the actual moment of inertia of the pulley based on your measurement)

The mass of the pulley is concentrated toward the center

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