Part I. Essentials, 5 points each
Note: In these problems you will write the appropriate equation, solve for the desired quantity, and substitute in the appropriate numbers, do NOT solve for the final number, nobody cares.

1. Moment of Inertia: (rotational mass) Determine the rotational mass of the system of masses in the figure if the system is pivoted about an axis perpendicular to the plane containing the masses and thru the center mass.

2. Conservation of momentum
A missile is travelling west at 200 m/s when it suddenly explodes. If two thirds of the missile recoils east at 50 m/s, what is the final velocity of the other one third of the missile?

3. A sphere of mass 50 kg and radius 3 m rolls along the ground at 8 m/s. What is it's total kinetic energy?
4. t =Ia=rF sinu
A 50 kg pulley is a disk of radius 3 m . It has a rope that is wrapped around it's outer rim several times. What will be the acceleration of a 40 kg mass attached to the end of the rope and released ?

5. Impulse-momemtum:
If a 5 kg object has an initial velocity of 20 m/s. If a force of 50 N is applied to this object for 15 seconds, what will be its final velocity?

6. Conservation of angular momentum:
Fido the fat (200 kg) is sitting on a stationary merry-go-round. When Fido begins galloping clockwise around the merry-go-round a distance of 2 m from the center at a speed of 4 m/s, the merry-go-round rotates in the opposite direction 2 rad/s, what must be it's moment of inertia?

7. t = r F sin u. A 3 m rod pivots about one end. A force of 20 newtons is applied to the other end at an angle of 30° with the direction of the rod. What is the torque produced by this force?

8. Work
A kid pulls a 50 kg rock 20 m up the incline as indicated in the picture. How much work does she do on the rock?

Part II. The Nitty Gritty: 10 points each

1. Really nasty can't believe he'd do this to us Rot Kinetic Energy problem.

We have here a massless hoop system, with 8 masses m attached as shown. It begins from the top of the incline that is 5 m high with initial speed v0 = 20 m/s, how fast is it going when it reaches the bottom?

2. Definitions: Aft thrust engines propel a craft forward, forward thrust engines propel a craft backwards .
A 106 kg space ship is moving forward at 500 m/s. A forward thrust engine that produces a force of magnitude 5 x 106 N is employed for 40 seconds used to slow down the space ship.

a. What is the final velocity of the space ship?
b. How much energy was used in this manuver ?
c. What is the power output of the engine (assuming 100 % efficient)?

3. A woman whose mass is 90 kg stands at the rim of a horizontal turntable having a moment of inertia of 500 kg m2 and a radius of 2m. Beside her is her faithful but very obese dog Fido, who's mass is 180 kg. The system is initially at rest, and the turntable is free to rotate about a frictionless, vertical axle through its center. The woman releases her pet Fido who begins to gallop in the counterclockwise direction at a speed of 4 m/s at a distance of 1 m from the rim. How fast must the lady jog around the outside rim of the turntable to keep it from rotating?

4. A 50 kg cart rolls down an incline as indicated in the picture. It starts from rest at a position that is a vertical distance of 45 m above the bottom of the incline. If it's speed when it gets to the bottom of the incline is only 20 m/s, what is the constant friction force caused by bad bearings in the wheels?