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:

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the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form