A physics student runs along a line tangent to the edge of a motionless merry-go-round and jumps on at the very outside. The merry-go-round has the shape of a uniform disk. A) Make an angular momentum chart to help you keep track of what is and is not changing. Consider the two objects, the student and merry-go-round, with the total angular momentum of these two objects conserved. Must the student have angular momentum before jumping on the merry-go-round?
B) Is linear momentum conserved in this interaction if you just consider the merry-go-round and the student?

We know that angular momentum is mvr

So that of the students initially will be

A1= mvr

and the final of the student and the merrygo round will be

A2= (1/2Mr²+mr)omega

So

Angular velocity (omega)= mvr/(1/2Mr²+mr)

This is the final angular velocity of the system so yea the student must have angular momentum before jumping on the merry-go-round

B. Because of directional changes at every edge of the Merry go round that result in changes in velocity, this results in changes in momentum too thus linear momentum is not conserved

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft