You have a pulley 11.9 cm in diameter and with a mass of 1.5 kg. You get to wond

Question

You have a pulley 11.9 cm in diameter and with a mass of 1.5 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 1.0 kg physics book 1.2 m above the floor. With your stopwatch, you can find that it takes 0.72 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?

Explanation / Answer

Here ,

for the uniform pulley ,

moment of inertia = 0.5 * m* r^2

moment of inertia = 0.5 * 1.5 * (0.119/2)^2

moment of inertia = 2.66 *10^-3 Kg.m^2

-------------------

let the acceleration is a

d = 0.5 at^2

1.2 = 0.5 * a * 0.72^2

a = 4.63 m/s^2

now , for the acceleration

a = mg/(m + I/r^2)

4.63 = 1.5 * 9.8/(1.5 + I/(0.119/2)^2)

solving for I

I = 5.93 *10^-3 Kg.m^2

the moment of inertia is 5.93 *10^-3 Kg.m^2

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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