Consider a stainless steel annular disk with an outer radius 68 mm and inner rad

Question

Consider a stainless steel annular disk with an outer radius 68 mm and inner radius 7.4 mm. The mass of the disk is 1349 grams. (b) The stainless steel annular disk is allowed to rotate on a frictionless table with the rotation axis at its center. The disk has a small cylinder rigidly mounted at the top concentrically. The cylinder's radius is 12.5 mm, and the mass of the cylinder is negligible. A string is wrapped around the cylinder, and a hanging mass of 19.3 g is tied at the other end of the string. When the mass falls under gravity, it causes the stainless steel annular disk to rotate. Ignoring the string's mass, and assuming that the string's motion is frictionless, what is the angular acceleration of the stainless steel annular disk? rad/s2 (c) What is the angular speed of the stainless steel annular disk 4.4 seconds after the hanging mass is released from rest? rad/s (d) At what speed is the hanging mass falling at this time? m/s (e) What is the kinetic energy of the falling mass at this time? J (f) What is the rotational kinetic energy of the stainless steel annular disk at this time? J (g) How much distance has the hanging mass been falling by this time? m

Explanation / Answer

msg*r = I

19.3*10-3 *9.8*12.5*10-3 = 1/2 1.349*(682-7.42)*10-6*

=0.767 rad/s2

c)=/t

=63.55/4.4 =0.1743rad/s

d) v= r= 68-7.4 * 0.1743=10.560m/s

e)K.E= 1/2mv2

f)R.E= 1/2 I 2

g)mgh=1/2 mv2

h is the distance fallen

cheers :)

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