Calculating Final Velocity of a Yo-Yo Dropped from 0.8 m

[Menisto]

A yo-yo of mass .3 Kg with a radius .03 m spins on an axel of radius .02 meters. It is dropped a distance .8 m, what is its final velocity?

I started:

mg -T=ma
mr(0)t = I(alpha)-->(alpha)= a/r

So:

mg - (Ia)/mr(0)^2 = ma

a = mg/ (m + I/(mr(0)^2)

I = 1/2 mR(1)^2

I checked over this numerous times and was unable to find my error, but I keep getting 2.06 for acceleration. The acceleration that would lead to the correct answer is 4.6 (m/s^2).

 

[OlderDan]

A yo-yo of mass .3 Kg with a radius .03 m spins on an axel of radius .02 meters. It is dropped a distance .8 m, what is its final velocity?

I started:

mg -T=ma
mr(0)t = I(alpha)-->(alpha)= a/r

So:

mg - (Ia)/mr(0)^2 = ma

a = mg/ (m + I/(mr(0)^2)

I = 1/2 mR(1)^2

I checked over this numerous times and was unable to find my error, but I keep getting 2.06 for acceleration. The acceleration that would lead to the correct answer is 4.6 (m/s^2).

Everything you have said looks correct. I cannot see an error that would lead to the answer you got, but you must have made an algebra mistake. I got a = 4.6m/s^2