Answer
The magnitude of the linear acceleration of the yo-yo during its rise is $~~6.5~m/s^2$
Work Step by Step
We can approximate the yo-yo as a uniform disk. We can write an expression for the rotational inertia:
$I = \frac{1}{2}MR^2$
Note that the magnitude of acceleration of a yo-yo is the same during its fall and its rise.
We can use Equation (11-13) to find the magnitude of the linear acceleration of the yo-yo during its rise:
$a = \frac{g}{1+I/MR^2}$
$a = \frac{g}{1+\frac{1}{2}MR^2/MR^2}$
$a = \frac{g}{1+\frac{1}{2}}$
$a = \frac{2g}{3}$
$a = \frac{(2)(9.8~m/s^2)}{3}$
$a = 6.5~m/s^2$
The magnitude of the linear acceleration of the yo-yo during its rise is $~~6.5~m/s^2$
