https://baixardoc.com/documents/ebooksclub-org-essential-university-physics-2nd-edition-ibrahim--5d0bed3e2f53d said:
■ On the Playground A merry-go-round is rotating freely when a boy runs radially inward, straight toward the merry-go-round’s center, and leaps on. Later, a girl runs tangent to the merry-go-round’s edge, in the same direction the edge is moving, and also leaps on. Does the merry-go-round’s angular speed increase, decrease, or stay the same in each case? EVALUATE Because the merry-go-round is rotating freely, the only torques are those exerted by the children as they leap on. If we consider a system consisting of the merry-go-round and both children, then those torques are internal, and the system’s angular momentum is conserved. In Fig. 11.7 we’ve sketched the situation, before either child leaps onto the merry-go-round and after both are on board. The boy, running radially, carries no angular momentum (his linear! momentum and the radius vector are in the same direction, making L zero), so you might think he doesn’t change the merry-go-round’s angular speed. Yet he does, because he adds mass and therefore rotational inertia. At the same time he doesn’t change the angular momentum, so with I increased, v must therefore drop. Running in the same direction as the merry-go-round’s tangential velocity, the girl clearly adds angular momentum to the system—an addition that would tend to increase the angular speed. But she also adds mass, and thus increases the rotational inertia—which, as in the boy’s case, tends to decrease angular speed. So which wins out? That depends on her speed. Without knowing that, we can’t tell whether the merry-go-round speeds up or slows down. ASSESS The angular momentum the girl adds is the product of her linear momentum mv and the merry-go-round’s radius R, while she increases the rotational inertia by mR2. With small m and large v, she could add a lot of angular momentum without increasing the rotational inertia significantly. That would increase the merry-go-round’s rotation rate. But with a large m and small v—giving the same additional angular momentum—the increase in rotational inertia would more than offset the angular momentum added, and the merry-goround would slow down. We can’t answer the question about the merry-go-round’s angular speed without knowing the numbers.
