Two different balls are rolled (without slipping) toward a common finish line. T

Question

Two different balls are rolled (without slipping) toward a common finish line. Their angular speeds are shown to the right. The first ball, which has a radius of 7.13 cm, is rolling along a conveyor belt which is moving at 1.69 m/s and starts out 9.17 m from the finish line. The second ball has a radius of 4.68 cm and is rolling along the stationary floor. If the second ball starts out 6.44 m from the finish line, how long does each ball take to reach the finish line? What angular speed would the losing ball have needed to cross the finish line at the same time as the winning ball?

Explanation / Answer

for the first time you should find v1

v1=w1r1+vbelt=(the angular speed for the first one from the graph)*0.0713+1.69

t1=d1/v1=9.17/v1

the second time:

v2=w2*r2=(w2 from the graph)*0.0468

t2=d2/v2=6.44/v2

for the angular speed:

v=d2/t1=6.44/t1

then u have to convert it to the rad/s by deviving it with r2

v/0.0468= the angular speed

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