A rotating uniform-density disk of radius 0.8 m is mounted in thevertical plane. The axle is held up by supports that are not shown,and the disk is free to rotate on the nearly frictionless axle. Thedisk has mass 4.4 kg. A lump of clay with mass 0.3 kg falls andsticks to the outer edge of the wheel at location A, < -0.56,0.571, 0 > m. Just before the impact the clay has a speed 8 m/s,and the disk is rotating clockwise with angular speed 0.48radians/s.The picture of the wheel can be find at this website:http://www.webassign.net/mi3/11-086-clay_ball_hits_disk.jpga). Just before the impact, what is the angular momentum of thecombined system of wheel plus clay about the center C? (As usual, xis to the right, y is up, and z is out of the screen, towardyou.)< , , > kgm^2/sb). Just after the impact, what is the angular momentum of thecombined system of wheel plus clay about the center C?< , , > kgm^2/s

OneClass: A rotating uniform-density disk of radius 0.8 m is mounted in thevertical plane. The axle i...

A wad of sticky clay with mass "m" and a velocity vector is fired at a solid cylinder of mass "M" and radius "R" as in the figure. The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d<R from the center.

Find the angular speed of the system just after the clay stikes and sticks to the surface of the cylinder?
Is the mechanical energy of the clay-cylinder system constant in the process?

olivebutterfly197

A playground ride consists of a disk of mass M = 56 kg and radius R= 2.0 m mounted on a low-friction axle. A child of mass m = 21 kgruns at speed v = 2.8 m/s on a line tangential to the disk andjumps onto the outer edge of the disk.

ANGULAR MOMENTUM
(a) Consider the system consisting of the child and the disk, butnot including the axle. Which of the following statements are true,from just before to just after the collision?
The momentum of the system doesn't change.
The momentum of the system changes.
The axle exerts a force on the system but nearly zero torque.
The torque exerted by the axle is zero because the force exerted bythe axle is very small.
The angular momentum of the system about the axle changes.
The angular momentum of the system about the axle hardlychanges.
The torque exerted by the axle is nearly zero even though the forceis large, because || is nearly zero.

(b) Relative to the axle, what was the magnitude of the angularmomentum of the child before the collision?
|C| = kgÂ·m2/s
(c) Relative to the axle, what was the angular momentum of thesystem of child plus disk just after the collision?
|C| = kgÂ·m2/s
(d) If the disk was initially at rest, now how fast is it rotating?That is, what is its angular speed? (The moment of inertia of auniform disk is Â½MR2.)
= radians/s
(e) How long does it take for the disk to go around once?
Time to go around once = s
ENERGY
(f) If you were to do a lot of algebra to calculate the kineticenergies before and after the collision, you would find that thetotal kinetic energy just after the collision is less than thetotal kinetic energy just before the collision. Where has most ofthis energy gone?
Increased chemical energy in the child.
Increased thermal energy of the disk and child.
Increased translational kinetic energy of the disk.

MOMENTUM
(g) What was the speed of the child just after the collision?
v = m/s
(h) What was the speed of the center of mass of the disk just afterthe collision?
vcm = m/s
(i) What was the magnitude of the linear momentum of the disk justafter the collision?
|p| = kgÂ·m/s
(j) Calculate the change in linear momentum of the systemconsisting of the child plus the disk (but not including the axle),from just before to just after impact, due to the impulse appliedby the axle. Take the x axis to be in the direction of the initialvelocity of the child.
px = px,f - px,i = kgÂ·m/s

ANGULAR MOMENTUM
(k) The child on the disk walks inward on the disk and ends upstanding at a new location a distance R/2 = 1 m from the axle. Nowwhat is the angular speed? (It helps to do this analysisalgebraically and plug in numbers at the end.)
= radians/s
ENERGY
(l) If you were to do a lot of algebra to calculate the kineticenergies in part (k), you would find that the total kinetic energyafter the move is greater than the total kinetic energy before themove. Where has this energy come from?
Decreased chemical energy in the child.
Decreased momentum of the disk.
Decreased thermal energy of the disk and child.

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