To determine the resulting velocity, we can use the principle of conservation of angular momentum. First, calculate the initial angular momentum of the system by finding the moment of inertia of the carriage and the cylinder. Then, use the equation L = Iω to find the final angular velocity. Finally, convert the angular velocity to linear velocity using v = ωR.
To determine the resulting velocity of (a) the carriage and (b) the center of the cylinder, we can use the principle of conservation of angular momentum. First, let's calculate the initial angular momentum of the system, which is given by the product of the moment of inertia and the angular velocity. The moment of inertia of the system is the sum of the moment of inertia of the cylinder and the moment of inertia of the carriage. For the carriage, the moment of inertia is given by I = MR^2, where M is the mass of the carriage and R is the radius. For the cylinder, the moment of inertia is I = (1/2)MR^2, since it rolls without sliding. After calculating the initial angular momentum, we can use the equation L = Iω to find the final angular velocity of the system. Finally, we can convert the angular velocity to linear velocity using the equation v = ωR.