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

International Edition---engineering Mechanics: Statics, 4th Edition
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Author:Andrew Pytel And Jaan Kiusalaas
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Chapter7: Dry Friction
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Problem 7.26P: The uniform plank is initially at rest on the fixed support at A and the stationary drum at B. If...
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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.
Transcribed Image Text: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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