The kinematics equations for angular motion are exactly analogous to the linear equation. Imagine the question gave you a known velocity and acceleration and asked you to find the stopping distance. You would use the equation V^2=Vo^2+2*a*d and solve for d.

With angular motion, the equation is the same: w^2=wo^2 + 2 (alpha)( theta_f - theta_i)

Solve this for the change in angle. Then remember that a change of 2*pi radians is one revolution

Hope this helps!

This is a classic Faraday's Law problem! Remember that the emf produced is the negative of changing magnetic flux with time. Start by writing the magnetic flux as the magnetic field times the area formed by the two rails, the resistor, and the metal bar. How can you find the change of this flux per time? One strategy is to write the position of the bar at time t = 0 as x_0, and the position at time t = Δt as x_0 + v * Δt. Then you can write the change in area ΔA = L * Δx. From here, divide by Δt and multiply by the magnetic field B to find the rate of change of the flux.

Now you should be equipped to find the emf and use Ohm's law to write the current in terms of the emf and the resistance. Finally, you can plug in all the numbers you have and solve for what you need.

The center of mass is computed by summing the mass of a system times its position. In other words, it's a quantity that depends on the distribution of mass. As such, the actual center of mass doesn't have to correspond to a point where mass actually exists! Consider a boomerang-shaped object that is heavier on the ends than near the center. The distribution of mass will be skewed towards the open region of space on the inside of the curve. In essence, this approach is what a jumper can do to avoid coming in contact with the bar while not having to get their center of mass above the bar!

The force of friction depends on the coefficient of friction and the normal force. In this situation, we'll assume that the coefficients are equal, which means that the setup that involves a greater normal force will create a stronger frictional force.

What is it that creates the normal force? Gravity pulls the ladder down, and the floor and wall provide normal forces. If the ladder is mostly upright, the normal force from the floor has to provide most of the vertical force opposing gravity, so we would expect the force of friction with the floor to be greater. What does that tell you about the safety?

Kepler's laws are really just a consequence of Newton's laws! In other words, they are Newton's laws applied to the case of orbital motion. If you want to see a proof, you will have to take a course in dynamics!

What you would learn is that the inward force of gravity pulls other objects along a trajectory that can be described geometrically. If the energy of the object is high enough, it will travel along a parabolic or hyperbolic curve. But if the energy is low enough, the object will be stuck in an orbit that is either elliptical or circular. In the case of Kepler's first law, the Sun is so massive compared to the planets that the Sun is barely affected by the gravity of the planets.

For any collision, the thing you always need to remember is that momentum is conserved. You made a good start with conservation of Kinetic Energy for this elastic collision, but to solve this you will need to add in the conservation of momentum. Also, remember that momentum is a vector so you will need to treat the x and y momentums separately.

I am not sure I completely understand the question, so I will try to answer a few things that might be going on here. Relativistic physics refers to dealing with kinematics and energy at very high speeds. Since nothing can move faster than the speed of light, physics gets (for lack of a better word) weird at speeds near the speed of light. If you are wondering how relativistic physics work with slower speeds, the answer is that technically the complicated relativistic equations apply for all speeds its just that at low speeds we can approximate the equations to equal the ones we are used to.

If you are instead wondering about the general idea of relativity that relativistic physics come from, there is something called Galilean relativity. This is the idea that the laws of motions are the same in all reference frames, or more simply that you can view any object (moving or otherwise) as being at rest and change the velocity and position of every other object accordingly and physics still works the same. With this, many 1-D kinematic equations become much easier, as two trains moving towards each other can be interpreted as one very fast train coming at a motionless train and the answer will be the same.

Hopefully you were wondering about one of those and not another interpretation that is eluding me.

It actually does not. Elastic or inelastic will change how the velocity is split between the two masses, but in every collision momentum has to be conserved. If you simply look at the momentum of the system (the system mass times the center of mass velocity), then momentum has to be constant because the only interactions are within the system. So as long as momentum is conserved, center of mass velocity is a constant regardless of the nature of the collisions within the system.

I won't go deep into this, but this is actually a very important observation. Your instinct is correct that the elevator going up will cause the screw to seem faster. And while it may seem counterintuitive because they are in different directions, you can just add the acceleration due to gravity to the magnitude of the elevators acceleration to get an equivalent acceleration of the screw.

This is called a reference frame. Rather than looking at the elevator and the screw both moving, you can act as if the elevator is still (as it seems to anyone standing in the elevator) and subtract the acceleration of the elevator from the accelerations of every other object. (note here I said subtract the accelerations rather than add because I am talking about the acceleration as a vector rather than just the magnitude as I was before)

Well, first I would recommend to not be doing physics mindlessly. The most common mistakes come from making assumptions to speed up the problem. That being said, your first step should be finding the equation(s) to use. This problem gives you v_0, a by assumption of gravity, and a distance, so you will want to find an equation or set of equations that has all of these plus t (which you want to solve for). So the best candidate is

x_f=a/2*t^2+v_0+x_0 (x_0 can be assumed to be 0)

However, you don't have an actual value for x_f, so first you need to find that. The hint in this problem is that it is the highest point. At the highest point in a throw, the vertical velocity is 0, so this gives us another variable to use in equation finding. This will lead us to

v_f^2-v_i^2=2*a*(x_f-x_0)

From this we can get x_f in terms of variables we know and then plug the answer back into the first equation. This will give us an equation made of only variables we know and the one we want.