physics
posted by igore .
Force, Work, and Rotation Question? Please Help!?
You are sitting on a stool that is free to rotate without friction, and you are holding a 2.0 kg weight in each hand (ignore friction and all forces external to you + weights system). Also ignore your own moment of inertia (pretend your moment of inertia is zero and that the moment of inertia of the you + weights system is determined entirely by the weights). You and your weights are rotating with an angular velocity of 3 radians per second, and you are holding the weights with arms outstretched so that each is 80.0 cm from the axis of rotation ( that is the distance from the axis to the center of mass of each weight). Then you pull your arms in so that weights are 20.0 cm from the axis of rotation.
a) What happens and why?
b) What is your angular velocity after you pull your arms in?
c) Keeping in mind what is and is not conserved as you pull in your arms, what are the initial and final kinetic energies of the rotating system?
d) Let the initial angular momentum of the system be L, the mass of one of the weights be M, and the distance from the axis of rotation to the blocks be R. (Note that if the angular momentum of the system is L, then the angular momentum of one of the blocks is L/2)
Then show that the force required to pull one of the blocks in at constant speed is equal to:
F=L^2/(4MR^3)
e) Now show that the magnitude of the work required to pull the blocks in from a distance of 80.0 cm to a distance of 20.0 cm really is equal to the difference in kinetic energy that you calculated in part c. That is, even if you couldn't derive it, use the formula for force given above and calculate the work done as you pull in the weights. Do not use conservation of energy to assert that the work is equal to the change in kinetic energy. Calculate the work done (using force as a function of distance) to show that it really is equal to the change in kinetic energy. There is an integral involved.
Thank you very much for any help for the above questions. Due tomorrow. Hopefully, my answers comes out like yours.
Respond to this Question
Similar Questions

physics
A 2.0kg block is sitting on a 15 degree incline. The coefficient of friction is 0.22. What is the minimum force needed to cause the block to accelerate UP the slope? 
physics helppp!
The coeffcient of friction between the 7.9 kg mass and the table is 0.55, and the coeffcient of friction between the 5 kg mass and the table is 0.38. Consider the motion of the 37 kg mass which descends by the amount of y = 0.45m after … 
physics
A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the studentstool system is 4.6 kg m^2. A second student tosses a 1.5 kg mass with a speed of 2.9 m/s to the student on the stool, who … 
physics
A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the studentstool system is 4.2 . A second student tosses a 1.1 mass with a speed of 3.0 to the student on the stool, who catches it … 
physics
A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the studentstool system is 4.6 kg m^2. A second student tosses a 1.5 kg mass with a speed of 2.9 m/s to the student on the stool, who … 
physics MC QUESTIONS
1. You push a block up a ramp with friction. The block is moving at constant speed ? 
physics MC QUESTIONS
Can you help please Question1: A car makes a banked turn on a "real" road (meaning you can not ignore friction), which of the following are forces that act on the car: (for full credit you must select ALL that are true) A)centripetal … 
physics plz
Can you help please Question1: A car makes a banked turn on a "real" road (meaning you can not ignore friction), which of the following are forces that act on the car: (for full credit you must select ALL that are true) A)centripetal … 
physics
Consider the system shown, with m1 = 2.0 kg, m2 = 3.0 kg, and á = 30o. The force F acts horizontally to the left and the kinetic coefficient of friction between m1 and the incline is ìk = 0.40. The mass m2 is moving up at a constant … 
physics
A 300 kg boulder is dragged 8 m across level ground with a chain that makes an angle of 37° with the horizontal. If the applied force on the chain is 800 N and there is a coefficient of friction of 0.20, find (a) the work done by …