Question
Asked Nov 5, 2019
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Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the angular acceleration when it has an angle of 10.0 degrees from the vertical?

 

Calculate the time t for the pencil to hit the ground, assuming that it falls from standing perfectly vertical and maintains this angular acceleration.
Express your answer in seconds.
 
a=-17.0 rad/s2
Known
+
10.0 g
0 cm
7.5 cm
rw
0-10.0
980 m/s2
N
rw
Axis
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Known + 10.0 g 0 cm 7.5 cm rw 0-10.0 980 m/s2 N rw Axis

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Expert Answer

Step 1
Given
1 kg = 10003
1m=100 cm
2
mam of the pen ci m- 10.0g
10008
Acceleralfon due to gaovity, g- 9. 8o m/s
Distante of center ofmoss from the balanced pcint
0.075m
io7.5cm (
=0.15 m
Lengh of penef L = 2 Tis 2(7.5 cm)o ,
Ineinatfon angle pom the veatilal, 0= lo
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Given 1 kg = 10003 1m=100 cm 2 mam of the pen ci m- 10.0g 10008 Acceleralfon due to gaovity, g- 9. 8o m/s Distante of center ofmoss from the balanced pcint 0.075m io7.5cm ( =0.15 m Lengh of penef L = 2 Tis 2(7.5 cm)o , Ineinatfon angle pom the veatilal, 0= lo

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Step 2
Initfally pencil i Afandins pesfecfly vertcal, then it began
to fall. The het torgue octfng om the pensil due to the
gpavitationl forte at t Cente of pencil,
Torque(forte) L dia tan te fom the axts)
mgsine
(mg stne)()
Thet
help_outline

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Initfally pencil i Afandins pesfecfly vertcal, then it began to fall. The het torgue octfng om the pensil due to the gpavitationl forte at t Cente of pencil, Torque(forte) L dia tan te fom the axts) mgsine (mg stne)() Thet

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Step 3
Net togue acting on the pentil due to avitation fos ce
wauld gire the pencile angulor accelesation. (a)
Apply NewtonseCond law of otatiom
Z Tnet = Io
TneHa of thin rod at the end, Im
when, m th mass, and LA ho lengh
1
help_outline

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Net togue acting on the pentil due to avitation fos ce wauld gire the pencile angulor accelesation. (a) Apply NewtonseCond law of otatiom Z Tnet = Io TneHa of thin rod at the end, Im when, m th mass, and LA ho lengh 1

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Science

Physics

Rotational Mechanics

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