A thin uniform rod with mass M = 4 kg kg is pivoted about one end as shown in the figures at right. Initially the rod is at rest in horizontal position. Then the rod is released from rest. At the instant the rod makes an angle 30° with the horizontal, the angular speed of the rod is w = /5 rad/s. (Ignore friction and air resistance) (Take g = 10m/s²) L M a) What is the moment of inertia of the rod about an axis passing through the pivot. (Upper figure at right) b) At the instant the rod makes an angle 30° with the horizontal, what is the tangential speed of the center of mass of the rod? L c) In the previous problem suppose that a small ball with mass m = 1 kg is glued to the center of the same rod as shown in the lower figure at right. Initially the rod with the ball is at rest in horizontal position. Then the rod with the ball is relased from rest. Does the moment of inertia of the system combining the rod and ball change? If it changes what is the value of it? M m

A thin uniform rod with mass M = 4 kg kg is pivoted about one end as shown in the figures at right. Initially the rod is at rest in horizontal position. Then the rod is released from rest. At the instant the rod makes an angle 30° with the horizontal, the angular speed of the rod is w = /5 rad/s. (Ignore friction and air resistance) (Take g = 10m/s²) L M a) What is the moment of inertia of the rod about an axis passing through the pivot. (Upper figure at right) b) At the instant the rod makes an angle 30° with the horizontal, what is the tangential speed of the center of mass of the rod? L c) In the previous problem suppose that a small ball with mass m = 1 kg is glued to the center of the same rod as shown in the lower figure at right. Initially the rod with the ball is at rest in horizontal position. Then the rod with the ball is relased from rest. Does the moment of inertia of the system combining the rod and ball change? If it changes what is the value of it? M m

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 60PQ

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