# Yo-yo: Vertical acceleration

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1. Dec 7, 2016

### Cepterus

1. The problem statement, all variables and given/known data
A yo-yo consists of two cylinders with radius $R$, mass $M$ and height $H$ connected by a smaller cylinder of radius $r$, mass $m$ and height $h$.

Determine the yo-yo's acceleration in $z$-direction, using its moment of inertia.

2. Relevant equations
Moment of inertia of a solid cylinder: $I=\frac12mr^2$

3. The attempt at a solution
The yo-yo's total moment of inertia is $I_{\text{tot}}=\frac12mr^2+MR^2$, using the formula for solid cylinders. However, I don't know how to proceed from here.

Last edited: Dec 7, 2016
2. Dec 7, 2016

### TSny

Free body diagram.
$\sum F = ma$.
$\sum \tau = I \alpha$.

3. Dec 7, 2016

### BvU

Hi Cep,

Could gravitational acceleration appear somewhere ?

4. Dec 7, 2016

### Cepterus

I guess so. The acceleration probably consists of both gravitational acceleration downwards and the acceleration upwards caused by the "user" of the yo-yo.
Is that what you mean?

5. Dec 7, 2016

### BvU

Yes. Make a sketch where the driving force acts and how it results in a torque.