1. An oversized yo-yo is made from two identical solid disks each of mass = 2.40

Question

1. An oversized yo-yo is made from two identical solid disks each of mass = 2.40 kg and radius R = 10.8 cm. The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system. a. What is the moment of inertia of the system? b. Write an equation for the angular acceleration (alpha) in terms of the translational acceleration a and radius r. c. Write Newton's second law for the system in terms of m, M, a, T, and g d. Write Newton's second law for rotation in terms of I,OHM, T and r. e. From these equations find the acceleration a. f. What is the tension in the string? g. How long does it take the system to drop 1.00 m from rest?

Explanation / Answer

Let the angular accn be A (anticlockwise)

Translational accn be a (downwards)

Tension be T(upward)

a) I = 0.5(mr^2 + 2MR^2)

       = 0.5(1*0.04^2 + 2*2.4*0.108^2)

       = 0.108 kgm^2

b) A = - a/r

c) T - (2M + m)g = (2M+m)a

d) T*r = I*A

e) -Ia/r^2 - (2M+m)g = (2M + m)a

=> a = - [(2M+m)g / (2M + m + I/r^2)]

I/r^2 = 0.5 m + MR^2/r^2

=> a = - [(2M + m)g / (M(2 + R^2/r^2) + 1.5m) ]

a = - 2.44 m/s^2

f) T = (2M + m)(g+a) = 43.85 N

g) s = 0.5*a*t^2

=> - 1 = - 0.5*2.44*t^2

=> t = 0.9 s

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