Why Is My Solution for Rotational Motion Incorrect?

[GreenPrint]

Homework Statement

Please see the attachment.

Homework Equations

The Attempt at a Solution

Please see the attachment. When I tried to solve the equations for a I got a different answer and I don't see what I'm doing wrong. Please let me know if you cannot follow my work. Thanks for any help you can provide.

 

[SammyS]

Illegal algebra cancellation.

$$\frac{MR^2}{2}\frac{a}{r}=(F_T)\,r$$

In the above equation, you canceled r on the left side with r on the right side.

 

[GreenPrint]

oh that's embarrassing thanks

 

[WJSwanson]

oh that's embarrassing thanks

Don't be embarrassed by it. Arithmetic and algebraic mistakes just plumb happen even to the best of us. I've had a professor who was the chair of my university's physics department and who performs nuclear physics experiments (specifically with lead nuclei, IIRC) at the LHC, and on occasion he made algebra errors when demonstrating examples on the board. Just go through stuff more slowly and carefully, and you should minimize the number of those mistakes that you make. :)