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

Question

An oversized yo-yo is made from two identical solid disks each of mass M = 2.40 kg and radius R = 10.4 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? Give a symbolic answer. (Use any variable or symbol stated above as necessary.)

moment of inertia =

(b) What torque does gravity exert on the system with respect to the given axis?

_____N·m Take downward as the negative coordinate direction.

(c) As depicted in the figure above, is the torque exerted by the tension positive or negative? (View the yo-yo from the left and let the counterclockwise direction be positive.) positive negative

(d) Is the angular acceleration positive or negative? positive negative

(e) What about the translational acceleration? positive negative

(f) Write an equation for the angular acceleration (alpha) in terms of the translational acceleration a and radius r. (Watch the sign!) = (g) Write Newton's second law for the system in terms of m, M, a, T, and g. (Do this on paper. Your instructor may ask you to turn in this work.)

(h) Write Newton's second law for rotation in terms of I, , T, and r. (Do this on paper. Your instructor may ask you to turn in this work.)

(i) Eliminate from the rotational second law with the expression found in part

(f) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R.

a =

(j) What is the numeric value for the system's acceleration?

_______m/s2

(k) What is the tension in the string?________ N

(l) How long does it take the system to drop 0.80 m from rest?

______s

Explanation / Answer

since the probelm contains more number of sub parts As per guide lines I am working first four parts

(a)

the moment of inertia is

I = 1/2 ( mr^2 + 2 MR^2) = 1/2 ( (1*0.04^2 + 2*2.4*0.104^2) = 0.02675 kg m^2

(b) torque by gravity is zero T = 0

(c) positive

(d) positive

(e) negative and direction is down ward

(f) = -a/r

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

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