A flat smooth disk has a radius of 18.0 cm, and can rotate around its center. On

Question

A flat smooth disk has a radius of 18.0 cm, and can rotate around its center. On the edge of the disk is a small metal weight of mass 480 gm, at rest relative to the disk. The coefficients of friction between the disk and the weight are mu = 0.520 and mu_d = mu_k = 0.380. The disk begins at rest, and accelerates at an angular rate of acceleration of alpha = 0.600 s^-2. At what angular velocity does the weight fly off of the disk? What is the angular displacement from the moment the disk begins to accelerate until the weight flies off of the disk?

Explanation / Answer

(A) maximum acc block can have, a = us g = 0.520 x 9.8 = 5.10 m/s^2

tagential acc, at = alpha r = 0.6 x 0.18 = 0.108 m/s^2

and a^2 = at^2 + ac^2

5.10^2 = 0.108^2 + ac^2

ac = 5.09 m/s^2 ...this is the maximum radial acc that block can have.

ac = w^2 r

5.09 = w^2 (0.18)

w = 5.32 rad/s

(B) wf^2 - wi^2 = 2 (alpha) (theta)

5.32^2 - 0 = 2 (0.6) (theta)

theta = 23.6 rad

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