I can't solve this physics problems, i've been trying for 2 days straight and i still can't solve them, i had to rewrite the questions because my handwriting is horrible, this is basically a repost with another image, my teacher isn't answering questions either so i am lost with this problems

The 20@kg wheel has a radius of gyration about its center g of kg = 300 mm. when it is subjected to a couple moment of m = 50 n # m, it rolls without slipping. determine the angular velocity of the wheel after its mass center g has traveled through a distance of sg = 20 m, starting from rest.

In physics the desire of an object to keep doing what it is doing is termed?

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele