You\'ve been given a pulley for your birthday. It\'s a fairly bigpulley, 12 cm i

Question

You've been given a pulley for your birthday. It's a fairly bigpulley, 12 cm in diameter and with a mass of 2.0 kg. You get towondering whether the pulley is uniform.
That is, is the mass evenly distributed, or is it concentratedtoward the center or near the rim?
To find out, you hang the pulley on a hook, wrap a stringaround it several times, and suspend your 1.0 kg physics book 1.0mabove the floor. With your stopwatch, you find that it takes 0.71sfor your book to hit the floor.
What can you conclude about the pulley?
That is, is the mass evenly distributed, or is it concentratedtoward the center or near the rim?
To find out, you hang the pulley on a hook, wrap a stringaround it several times, and suspend your 1.0 kg physics book 1.0mabove the floor. With your stopwatch, you find that it takes 0.71sfor your book to hit the floor.
What can you conclude about the pulley? That is, is the mass evenly distributed, or is it concentratedtoward the center or near the rim?
To find out, you hang the pulley on a hook, wrap a stringaround it several times, and suspend your 1.0 kg physics book 1.0mabove the floor. With your stopwatch, you find that it takes 0.71sfor your book to hit the floor.
What can you conclude about the pulley?
What can you conclude about the pulley?

Explanation / Answer

pulley diameter d = 12 cm = 12 * 10^-2 m mass M = 2.0 kg mass of physics book m = 1.0 kg height h = 1.0 m time taken to reach floor t = 0.71 s We know I * w = m * g * h or (M * r2/2) * w = m * g * h or w = (2m * g * h/M * r2) = (2m * g * h/M *(d/2)2) = (8m * g * h/M * d2) g = 9.8 m/s2 or w = (8 * 1.0 * 9.8 * 1.0/2.0 * (12 * 10^-2)^2) or w = 2722.2 rad/s the pulley rotates with an angular frequency w = 2722.2 rad/sand hence we can conclude that the mass is evenlydistributed. or w = (8 * 1.0 * 9.8 * 1.0/2.0 * (12 * 10^-2)^2) or w = 2722.2 rad/s the pulley rotates with an angular frequency w = 2722.2 rad/sand hence we can conclude that the mass is evenlydistributed.

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