I didn't do well on my $2$d test this semester. These are the problems I got wrong. My professor isn't helpful at all. Can you please walk me through how to solve each problem. I need to be able to understand it for the final exam. I really appreciate the help! Me understanding this unit$/$material could determine me passing or failing the class!

$$A disk of inertia $0\mathrm{.}10$ kg m$^2$ is rotating with an angular speed of $1\mathrm{.}0$ rad$/$s$.$ A non$-$rotating ring of mass $500\mathrm{.}0$ g and diameter of $80\mathrm{.}0$ cm is dropped onto the rotating disk. What is the new angular speed of this combination?$$

What is the total force on the bottom of a swimming pool $(20\mathrm{.}0$ m by $10\mathrm{.}0$ m$),$ if the pool has an average depth of $1\mathrm{.}50$ m$?$

A bicycle wheel undergoes a rotational motion at a constant rate of $1\mathrm{.}2$ rev$/$s$^2.$ If the wheel starts from rest, what is the wheel$$s rotational velocity and how many revolutions did the wheel turn after $4\mathrm{.}0$ seconds?

A $45\mathrm{.}0$ g disk with a $12\mathrm{.}0$ cm diameter slows down from $15$ rad$/$s to $11$ rad$/$s$.$ Find the work done on the disk to cause this action.

Calculate the gravity at $7,000\mathrm{.}0$ km above the Moon$$s surface.$$

A satellite of mass $300\mathrm{.}0$ kg is placed in orbit $300\mathrm{.}0$ km above the surface of Earth. Find the orbital velocity of the satellite.

At the low point in its swing,a pendulum bob has a velocity of $5\mathrm{.}0$ m$/$s$.$ How high will the bob swing above this low point?

A $255$ g cart is given an initial speed of $2\mathrm{.}35$ m$/$s at the base of an inclined plane, placed at$$ a $5\mathrm{.}50$ degree angle. Find the speed of the cart when it has traveled $34\mathrm{.}0$ cm up the incline. $($ignore friction$)$

A $7\mathrm{.}00$ g bullet is fired into a $2\mathrm{.}00$ kg ballistic pendulum of length $35\mathrm{.}0$ cm$.$ If the pendulum then rises to an angle of $32\mathrm{.}5$ degrees, what was the launch speed of the bullet?

A $1\mathrm{.}0$ kg object moving East at $5\mathrm{.}0$ m$/$s has an inelastic collision with a $2\mathrm{.}0$ kg object moving West at $10\mathrm{.}0$ m$/$s$.$ Solve for the velocity after impact.