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## Homework Statement

A yo-yo is pulled with a constant tension

*T*. The string is horizontal and parallel to the table and unwinding from the bottom of the spool, as shown. The yo-yo's outer radius is

*R*and the spool radius is

*r*. The mass of the yo-yo is

*m*and the moment of inertia of the yo-yo around the axis through its centre of mass is

*I*. What is the angular acceleration of the yo-yo, assuming it rolls without slipping?

2. Homework Equations

2. Homework Equations

α = τ

_{net}/ I

τ = Fsinθr

## The Attempt at a Solution

I think the spool rotates in the same direction as

*T,*but the rest of the yo-yo has to rotate in the opposite direction in order to roll without slipping.

*T*applies a negative torque, since it causes rotation in the CW direction, so τ

_{T}= -Tr

This is where I'm stuck. Is the inertia of the yo-yo just

*I*or is it

*I + mR*? And I'm not sure if it's only tension applying a torque to the yo-yo, or if the floor is exerting a backward force on the yo-yo to make it roll, and if so, is the force proportionate to the normal force. Can anyone please help me figure this one out?

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