I I) A 4.2-m-diameter merry-g o-round is rotating freely with a n angular velocity of 0.80 r ad/s. Its to tal m om ent of ine rtia is 1760 kg • m2. Four people standing on the ground, each of mass 65 kg, suddenl y step onto the edge of the merry-go-round. What is the angular velocity of th e merry-go-round now? W ha t if the people were o n it initially and the n jum ped off in a radial direction (relative to the merry-go -round)?

a) , b) A portion of the initial total energy is removed from system by the jump of the people and angular speed does not change. In other word, merry-go-round rotates slower.

Explanation:

a) Let assume that each person can be modelled as particles. The system is modelled after the Principle of Angular Momentum Conservation:

The angular speed is:

b) A portion of the initial total energy is removed from system by the jump of the people and angular speed does not change. In other word, merry-go-round rotates slower. According to the Principle of Energy Conservation, the phenomenon is observed:

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s