Rotational Motion dynamics problem

[miamirulz29]

Homework Statement

A giant yo-yo of mass 400 kg measuring about 1.2 m in radius was dropped from a platform 63 m high. One end of the string was tied to the platform, so the yo-yo unwinds as it descended. Assuming that the axle of the yo-yo has a radius of .1 m, find the velocity of descent at the end of the fall. the acceleration of gravity is 9.81. Answer in units of m/s.

Homework Equations

F = ma
Tau = I * alpha
I = mr^2/2

The Attempt at a Solution

mg-T = ma
rT = I * alpha
I solved for a and got a = 2g/3.

I then used that acceleration to find how the time it took to descend.
x = .5at^2, x being the height of the platform.

Once I found t, I found v using:
v = at.

The answer I got was incorrect. Could somebody please tell me what I am doing incorrectly? Thanks in advance.

 

[collinsmark]

Homework Equations

F = ma
Tau = I * alpha
I = mr^2/2

The Attempt at a Solution

mg-T = ma
rT = I * alpha
I solved for a and got a = 2g/3.

I'm not quite sure where you got your expression for a, but I came up with something much smaller.

A possible bit of advice is to take care with the fact that there are two 'r's involved.

• There's the 1.2 m radius of the entire yo-yo. This is important when calculating the yo-yo's moment of inertia, I.
• Then there is the 0.1 m radius of the axle. This is the one to use when torques and such are involved, like τ = Iα (where τ is the torque).
  [Edit: in other words, it's the 0.1 m radius of the axle -- not the 1.2 m radius of the entire yo-yo -- that relates torque to force (once the moment of inertia has already been calculated) and angular acceleration to linear acceleration.]