A yo-yo is made of two solid cylindrical disks, each of mass 0.055kg and diamete

Question

A yo-yo is made of two solid cylindrical disks, each of mass 0.055kg and diameter 0.071m , joined by a (concentric) thin solid cylindrical hub of mass 0.0048kg and diameter 0.012m .

Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.1m long string, if it is released from rest. (in m/s)
v=

What fraction of its kinetic energy is rotational? (%)
KErot/KEtot=

*5.69 m/s was not the correct answer after I tried solving myself so I need help with this questions along with the fraction

Explanation / Answer

m=75g =0.055kg d = 0.071M l=1.1m moment of inertia I =(1/2)mr^2 = (1/2)*0.055*(0.071/2)^2 = 3.46*10^-5 The decrease in potential energy equals the increase in kinetic energy, most of which is rotational KE. First compute the moment of inertia of the yo-yo, I. If it falls a distance L (which is 1.1 m in this case) then M g L = (1/2) I w^2 + (1/2) M V^2 The angular rotation rate w can be replaced by V/r, where r is the radius of the cylindrical hub. Then solve for V. V^2[1 + I/(Mr^2)] = 2*g*L V^2= 2*g*L /[1 + I/(Mr^2)] = 2*9.81*1.1/[1+3.46*10^-5/0.055*(0.071/2)^2] V^2 = 32.37 V= 5.69 m/s

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