Question

PRACTICE IT Use the worked example above to help you solve this problem. A merry-go-round modeled as a disk of mass M 9.00 x 101 kg and radius R = 2.50 m is rotating in a horizontal plane about a frictionless vertical axle (see figure) (a) After a student with mass m 88.0 kg jumps onto the merry-go-round, the system's angular speed decreases to 2.10 rad/s. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.450 m from the center. rad/s 5.82 (b) Find the change in the system's rotational kinetic energy caused by her movement to the center 3300 J (c) Find the work done on the student as she walks to r = 0.450 m. -940.95 J | I'M STUCK! EXERCISE HINTS: GETTING STARTED Use the values from the PRACTICE IT section to answer this exercise. (a) Find the angular speed of the merry-go-round before the student jumped on, assuming the student didn't transfer any momentum or energy as she jumped on the merry-go-round 8.079 X Angular momentum is conserved. There are some useful expressions in the example, but do not use all of them, since only some basic ones are valid. rad/s (b) By how much did the kinetic energy of the system change when the student jumped on? Notice that energy is lost in this process, as should be expected, since it is essentially a perfectly inelastic collision. KE- KE Need Help? Read It

Answer 1

6) Am = merry Georowd ine Me axlokg R=2.50m - Чоко ме P8 29 LOJ = Qilorades conservation of angular momentum b i = A + I) wt I = studeel- inertia Imawi = Gms + 2 m 2 ) Wf 3 902.50%ig: = ( 38(2.50)90 (2.505) 2.10) 281.25 w; = 1168225 (10;= 4.153 maddece ] Key Fe = le fwyaf 360° mitin = 2 ( mutam Rut - ( R )wi - (190(2503+ PP (2.50 5)(2.190(2:5)*)(4153) i 1832-9 - 2425.4) - - 592.516 J