212 Sample Exam # 4,
____________________
Do any three of the ff 4 problems:
1] A uniform square plate ( 2meter x 2meter; mass 6 kg) is pinned to the massless rod at O and is free to
rotate around the zaxis.
Find the angular acceleration
α
of the plate.
I
O
α
= Moment around O = Mg(meter /
√
2) =
=
6 x 9.81 /
√
2 = 41.62 Nm
I
O
= (I
C
=ML
2
/ 6) + M d
2
where d = 1 meter = d
OC
I
O
=
6 2
2
/ 6
+ 6 1
2
= 10 kg m
2
So,
α=4.16
rad / sec
2
2] The spool has a mass M and a radius of gyration of k.
Cords are wrapped around inner and outer surfaces at
r and R.
One is attached to the ceiling, the other to a mass m.
Neither cord slips.
Find the acceleration of m.
For full credit here it will suffice to find a set of purely algebraic eqns in a set of an equal number of unknown
scalar quantities, and to indicate that this set suffices to solve the problem.
T
2
R + T
1
r = Mk
2
α
where Mk
2
is I
cm
of spo
T
2
+ Mg T
1
= M a
M
mg  T
2
= ma
m
α
r = a
M
α
(R+r) = a
m
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View Full Document3] The Sshaped shaft consists of two halfrings, each of radius R=0.3meter and mass m/2 (m = 4kg).
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 Spring '10
 richard
 Force, Mass, Moment Of Inertia

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