Max (15 kg) and maya (12 kg) are riding on a merry-go-round that rotates at a constant speed. max is sitting on the edge of the merry-go-round, 2.4 m from the center, and maya is 1.2 m from the center. considering max and maya to be one system of masses, what is their moment of inertia measured with respect to 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.

Which statements about tornadoes are true? check all that apply. (a) about 12,000 tornadoes hit the united states every year. (b) a tornado looks like a funnel. (c) tornadoes are deadly atmospheric storms that cause millions in damages each year. (d) tornadoes can reach wind speeds of more than 300 miles per hour. (e) kansas is the state with the most tornadoes. (f) you will always notice a funnel before a tornado strikes.

(**i would really appreciate if this was answered soon** ) which pair of quantities includes one quantity that increases as the other decreases during simple harmonic motion?