A25.0-kg child is standing at the edge of a horizontal merry-go-round with a radius of 2.40 m and a moment of inertia of 356 kg∙m2 about a vertical axis through its center. the system (including the child) is initially rotating at 1.80 rad/s.
what is its angular velocity if the child moves to a new position 1.20 m from the center of the merry-go-round?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Aregion of space in which a measurable gravitational force is indicated by the force exerted on a test mass is called

Need asap ‼️ 20 pts which gravitational force field diagram is drawn correctly? (answers in pictures below)