Answer
The angular velocity of the wheel is $0.125~rad/s$
Work Step by Step
Initially, the angular momentum of the system is zero. By conservation of angular momentum, the angular momentum of the wheel is equal in magnitude to the angular momentum of the guinea pig about the axis.
Let $M$ be the mass of the wheel and let $m$ be the mass of the guinea pig. We can find the angular velocity of the wheel:
$I~\omega = mvR$
$\omega = \frac{mvR}{I}$
$\omega = \frac{mvR}{MR^2}$
$\omega = \frac{mv}{MR}$
$\omega = \frac{(0.500~kg)(0.20~m/s)}{(2.00~kg)(0.40~m)}$
$\omega = 0.125~rad/s$
The angular velocity of the wheel is $0.125~rad/s$.
