A yo-yo is made of two solid cylindrical disks, each of mass 0.053kg and diamete

Question

A yo-yo is made of two solid cylindrical disks, each of mass 0.053kg and diameter 0.078m , joined by a (concentric) thin solid cylindrical hub of mass 0.0054kg and diameter 0.010m .

1)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.

Express your answer using two significant figures.

v =

2)What fraction of its kinetic energy is rotational?

Express your answer using two significant figures.

KErot/KEtot=

Explanation / Answer

By energy methods, the initial PE will equal the KE rotational plus KE translational when it hits the end of the string

PE = mgh

KE rotational will be .5Iw2

We basically have three disks and each one has a moment of inertia defined as .5mr2, and w = v/r

Thus KE = .5(.5mr2)(v2/r2) for each disk

That simplifies to .25mv2

The individual masses are .053, .053, and .0054 which totals .1114 kg

So...

(.1114)(9.8)(1.1) = .25(.053)(v2) + .25(.053)(v2) + .25(.0054)(v2) + .5(.1114)(v2)

1.200892 = .08355v2

v = 3.8 m/s

Part B)

Rotational KE = .25(.053)(3.82) + .25(.053)(3.82) + .25(.0054)(3.82) = .40 J

Translational KE = .5(.1114)(3.8)2 = .80 J

Rotational/Trranslational = .40/.80

Rotational/Translational = .50 (Thus 50% is rotational)

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