Here are a few sample problems to prepare you for the third test:

1) You're investigating the scene of a car accident. Apparently a northbound car (1100 kg) and an eastbound pick-up truck (1800 kg) collided, stuck together, and slid 8 m, in a direction 27 degrees north of   east. If the coefficient of static friction between the wreck and the road is 0.8, what were the speeds of the two cars before they collided?

2) Let's revisit that last problem we discussed in class on Wednesday. Suppose we have a pulley (mass 2 kg, radius 6 cm), and a massless rope that passes over it without sliding. At the two ends of the rope are a 4 kg mass (1.0 m above the floor) and a 2 kg mass. Assuming there's no friction exerting a torque at the pulley's pivot, how long does it take for the 4 kg mass to hit the floor, assuming the whole assembly starts from rest? (This one is easy.)

3) The television networks rely on satellites to transmit their feeds. These satellites are always in the same part of the sky, so that a local affiliate need only point its dish once at the satellite. Where in the sky are these satellites (meaning which way do you point the dish), and how far above the earth are they?

4) We often consider a pendulum consisting of a massless string of some length with a point mass at the end. For that, the angular frequency is given by the square root of g divide by the length of the string, with no dependence on the mass. Suppose that instead we consider a pendulum consisting of a thin rod with mass m, pivoted at one end. Does the mass matter now? Is the frequency the same? If not, what is the frequency?

5) Suppose that instead of that little turntable we have in class, we had a nice big turntable, with a radius of 2 meters and a mass of 40 kg. Suppose that a student stands on it, right at the edge, and is initially stationary. This student (mass =60 kg) begins walking in a counterclockwise direction, at a rate of 1.1 m/s relative to the turntable. How fast is this student walking relative to the room?

6) Imagine that you have a pencil that's 20 cm long. Initially you support it at both ends, but then you remove one support and it of course falls, although the other end is supported (holds still) until the pencil is vertical. If that end is initially 1 m above the floor, through how many revolutions does the pencil turn before it hits the floor?

7) Always a good question: We have a 10 kg ladder, 2.5 m long, leaning against a wall. The ladder makes an angle of 70 degrees with the floor. Suppose the coefficient of static friction between the ladder and either surface is the same. A 60 kg painter needs to be able to clim halfway up this ladder without it slipping. What is the minimum friction coefficient that allows her to do this? OK, maybe this would be easier if the wall were frictionless - try that. Could we try a version where the floor is frictionless?