You have a pulley 14.7 cm in diameter and with a mass of 2.4 kg. You get to wond

Question

You have a pulley 14.7 cm in diameter and with a mass of 2.4 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 2.0 kg physics book 1.2 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?  

________________kg m2

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

Here,

radius ,r = 14.7 cm/2

r = 7.35 cm

mp = 2.4 Kg

m = 2 kg

d = 1.2 m

t = 0.58 s

if the moment of inertia is uniform

I1 = 0.5 * m * r^2

I1 = 0.5 * 2.4 * 0.0735^2

I1 = 6.483 *10^-3 Kg.m^2

the moment of inertia when pulley is uniform is 6.483 *10^-3 Kg.m^2

let the acceleation of the mass is a

Using second equation of motion

d = 0.5 * a * t^2

1.2 = 0.5 * a * 0.58^2

a = 7.134 m/s^2

Using second law of motion

a = m * g/(I/r^2 + m)

7.134 = 2 * 9.8/(2 + I/(0.0735^2))

solving for I

I = 0.00404 Kg.m^2

the actual moment of inertia of the pulley based on your measurement is 0.00404 Kg.m^2

-------------------
The mass of the pulley is concentrated toward the center   

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.