Rolling Ball IIB

See Rolling Ball I

See Rolling Ball IIA

A solid ball with a moment of inertia of $I=\frac{2}{5}mr^2$ is initially moving with a velocity of $v_i$ and it is sliding with no rotational motion at $t=0$ on flat ground (which you can assume to be extended to infinity).

The coefficient of kinetic friction is $\mu_k$ and coefficient of static friction is $\mu_s>\mu_k$ .

If the ratio of the final velocity to the initial velocity is $\frac{a}{b}$ , where $a$ and $b$ are coprime integers?

What is $a+b$ ?

note: (assume the ball to be rigid and the ground too, so you don't have to consider rolling friction.)

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See Rolling Ball IIIA