6. (2.5 points) An oversized yo-yo is made from two identical solid disks each o

Question

6. (2.5 points) An oversized yo-yo is made from two identical solid disks each of mass M = 1.90 kg and radius R = 10.1 cm. The two disks are joined by a solid cylinder of radius r= 4.00 cm and mass m = 1.00 kg. (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.) (b) What torque does gravity exert on the system with respect to the given axis? (c) Write an equation for the angular acceleration (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!) (d) Write Newton's second law for the system in terms of m, M, a, T, and g. (e) Write Newton's second law for rotation in terms of l, , T, and r.

Explanation / Answer

a] moment of inertia of system = 2*0.5MR^2+ 0.5 mr^2

I = MR^2 + 0.5 mr^2

b] torque by gravity = 0

c] alpha = a/r

d] 2Mg + mg - T = (2M+m)a

e] Tr = I alpha

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