Question

A playground ride consists of a disk of mass M = 59 kg and radius R = 1.9 m mounted on a low-friction axle. A child of mass m = 18 kg runs at speed v = 2.2 m/s on a line tangential to the disk and jumps onto the outer edge of the disk.

(b) Relative to the axle, what was the magnitude of the angular momentum of the child before the collision?
L|_C| =   
(c) Relative to the axle, what was the angular momentum of the system of child plus disk just after the collision?
L|_C| =  
(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 a uniform disk is ½MR².)
w =  
(e) How long does it take for the disk to go around once?

Time to go around once =  

MOMENTUM
(g) What was the speed of the child just after the collision?
v =
(h) What was the speed of the center of mass of the disk just after the collision?
v_cm =  
(i) What was the magnitude of the linear momentum of the disk just after the collision?
|p| =  
(j) Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including the axle), from just before to just after impact, due to the impulse applied by the axle. Take the x axis to be in the direction of the initial velocity of the child.
p_x = p_x,f - p_x,i =  

ANGULAR MOMENTUM
(k) The child on the disk walks inward on the disk and ends up standing at a new location a distance R/2 = 0.95 m from the axle. Now what is the angular speed? (It helps to do this analysis algebraically and plug in numbers at the end.)
w =  

Answer 1