Two identical tops spin with angular velocities 45 ? rad/s up and 19 ? rad/s dow

Question

Two identical tops spin with angular velocities 45? rad/s up and 19? rad/s down, respectively, about vertical axes on a table. The tops bump into one another and separate. After the collision, one of the tops has an angular velocity of 35? rad/s in its original direction.

What is the angular velocity of the other top if the 45? rad/s top ends up with the angular velocity of 35? rad/s? (Answer: -28.3rad/s)

What is the angular velocity of the other top if the 19? rad/s top ends up with the angular velocity of 35? rad/s? (Answer: 192rad/s)

Answers are provided above. Please show all work on how to get the answers.

Explanation / Answer

conservation of angular momentum

I1 w1 + I2 w1 = I1 w1 + I2 w2, but since I1 = I2

45 pi - 19 pi = 35 pi + w

w=-28.3 rad/s

b) now 45 pi - 19 pi = -35*pi+ w

w = 192 rad/s

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