TAKE:m=17kgL=7.60m The uniform bar has a mass m (given below) and length L (givenbelow). It is released from rest at an angle 0 as shown. Themoment of inertia of the rod about the pin point 0 is Io =÷ML².Neglect friction at 0.a) Determine the radius of gyration of the rod about the masscenter G.b) Draw the free-body diagram of the rod at the instant shown.c) Write the equations of motion, EF = måc, EMG = Içå, andEM, = Ioå, at the instant shown, in terms of the coordinatesystem given in the figure. (Do not solve the equations!)d) Determine the angular acceleration of the rod and the support reactions at 0 at the instantwhen 0 = 30°. [Solve the equations in part (c)!]GHint: Up to part (d), do not insert numbers (study parametrically). In part (d), insert numbers anduse åc = ảo + ả x ¡G/0 – w?¯G/o to connect the linear and angular quantities.

Answered: Image /qna-images/answer/1f61fe84-5650-40d5-84f4-0e519623ca4d.jpg

The uniform bar has a mass m (given below) and length L (given below). It is released from rest at an angle 0 as shown. The moment of inertia of the rod about the pin point 0 is Io =;mL². Neglect friction at 0. a) Determine the radius of gyration of the rod about the mass center G. b) Draw the free-body diagram of the rod at the instant shown. c) Write the equations of motion, EF = måc, EMc = Içå, and EM, = Ioå, at the instant shown, in terms of the coordinate system given in the figure. (Do not solve the equations!) ml?. %3D

The uniform bar has a mass m (given below) and length L (given below). It is released from rest at an angle 0 as shown. The moment of inertia of the rod about the pin point 0 is Io =;mL². Neglect friction at 0. a) Determine the radius of gyration of the rod about the mass center G. b) Draw the free-body diagram of the rod at the instant shown. c) Write the equations of motion, EF = måc, EMc = Içå, and EM, = Ioå, at the instant shown, in terms of the coordinate system given in the figure. (Do not solve the equations!) ml?. %3D

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

TAKE:

m=17kg

L=7.60m

The uniform bar has a mass m (given below) and length L (given
below). It is released from rest at an angle 0 as shown. The
moment of inertia of the rod about the pin point 0 is Io =÷ML².
Neglect friction at 0.
a) Determine the radius of gyration of the rod about the mass
center G.
b) Draw the free-body diagram of the rod at the instant shown.
c) Write the equations of motion, EF = måc, EMG = Içå, and
EM, = Ioå, at the instant shown, in terms of the coordinate
system given in the figure. (Do not solve the equations!)
d) Determine the angular acceleration of the rod and the support reactions at 0 at the instant
when 0 = 30°. [Solve the equations in part (c)!]
G
Hint: Up to part (d), do not insert numbers (study parametrically). In part (d), insert numbers and
use åc = ảo + ả x ¡G/0 – w?¯G/o to connect the linear and angular quantities.

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