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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

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 = V5 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?
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
m
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?
d) At the instant the rod is in vertical position, what is the
tangential speed of the point P (free end of the rod) in
terms of M (mass of the rod), g (gravitational acceleration),
L (the length of the rod), I (the moment of inertia of the rod
and ball system)
P.
O 21.33 kg.m^2
O 12 kg.m^2
O 3 kg.m^2
48 kg.m^2
5.33 kg.m^2
Diğer:

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