Solve Mechanical Physics Problems: Torque and Angular Velocity

[Dingo Jellybean]

I need serious help with these problems. They are all from Physics for Engineers and Scientist, 5th Edition by Paul Tipler.

5. [Tipler5 10.P.050.] A uniform cylinder of mass 105 kg and radius 0.5 m is mounted so that it turns without friction on its fixed symmetry axis. It is rotated by a drive belt that wraps around its perimeter and exerts a constant torque. At time t = 0, its angular velocity is zero. At time t = 25 s, its angular velocity is 450 rev/min. (c) What is the magnitude of the torque acting on the cylinder about the axis? (d) What is the magnitude of the force acting on the rim of the cylinder?

NOTE: I solved the first 2 parts. a) angular momentum about axis at t=25s is 618.5 kg m^2/s b) 24.74 kg m^2/s^2 is the rate of increase of angular momentum

So I need part c and part d. Thanks.



10.52) A space capsule is rotating about it's longitudinal axis at 6rev/min. The occupants want to stop this rotation. They have 2 small jets mounted tengentially at a distance 3m from the axis and can eject 10 g/s of gas from each jet with a nozzle velocity of 800 m/s. For how long must they turn on these jets to stop the rotation? The moment of inertia os the ship about it's axis is 4000 kg m^2.

10.P.058.] Two disks of identical mass but different radii (r and r2 = 1.8r) are spinning on frictionless bearings at the same angular speed W0 but in opposite directions. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular velocity. What is the magnitude of that final angular velocity in terms of W0? Note: W0 = Angular velocity(initial)

Tipler5 10.P.090.] Figure 10-55 shows a hollow cylindrical shell of length 1.8 m, mass 0.8 kg, and radius 0.2 m that is free to rotate about a vertical axis through its center and perpendicular to the cylinder's axis. Inside the cylinder are two thin disks of 0.17 kg each, attached to springs of spring constant k and unstretched lengths 0.4 m. The system is brought to a rotational speed of 15 rad/s with the springs clamped so they do not stretch. The springs are then suddenly unclamped. When the disks have stopped their radial motion due to fluid friction between the disks and the air in the cylinder, they come to rest 0.6 m from the central axis.
What is the angular velocity of the cylinder when the disks have stopped their radial motion? b) How much energy was dissipated in fluid friction between the disks and the air?

 

[Chen]

Question 10.52 was already answered on these forums:
https://www.physicsforums.com/showthread.php?t=17605

 

[arildno]

5. Use moment-of momentum equation.
10.5 P.058.
Use the moment-of momentum equation with respect to the center of mass (C.M);
it is positioned at the midpoint between the discs at the axis of rotation.
Only external forces contributes to moments around C.M; in your problem, these are the ones bringing discs together; neglect them!
Hence, the angular momentum of system about C.M is conserved. Note that the system's moment of inertia around C.M doesn't change in time, since the separation distance between the discs are along the rotational axis.