Adisk-shaped merry-go-round of radius 2.93 m and mass 165 kg rotates freely with an angular speed of 0.691 rev/s . a 62.4 kg person running tangential to the rim of the merry-go-round at 3.11 m/s jumps onto its rim and holds on. before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. calculate the final kinetic energy for this system

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.

What is the mass of the same rock on the earth

Acrow drops a 0.11kg clam onto a rocky beach from a height of 9.8m. what is the kinetic energy of the clam when it is 5.0m above the ground? what is its speed at that point?