The system consists of a thin blue disk with negligible mass and a radius r = 0.

Question

The system consists of a thin blue disk with negligible mass and a radius r = 0.92 cm attached to the gray disk with a radius R = 12.0 cm. The mass of the gray disk is M = 540 g.The two-disk system can only rotate about its center axis on a low-friction axle.

A small mass m = 82 g is attached to the system by wrapping a long string around the thin blue disk (think of a yo-yo). When the mass is allowed to fall, the mass pulls string off of the thin disk by rotating the system in a clockwise direction.

(a). What is the moment of inertia for this system?
I = kg

Explanation / Answer

a)

MOI = 1/2*MR^2 = 1/2*0.54*0.12^2 = 0.003888 kg-m^2

b)

Lrot = I = 0.003888*0.57 = 0.00221616 kg-m^2/s

Hence, <0, 0, 0.00221616>

c)

Torque = mg*r = 0.082*9.81*0.0092 = 0.0074 Nm

So, <0, 0, 0.0074>

d)

T = I

= T/I = 0.0074/0.003888 = 1.9 rad/s^2

= (2 - 1)/(t2 - t1)

1.9 = (2 - 0.57)/(1.3 - 0.3)

2 = 2.47 rad/s

Lrot = I = 0.003888*2.47 = 0.009617 kg-m^2/s

So, <0, 0, 0.009617>

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