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Unknowns:
T, a
Gy
,
α
Need another equation –
what can I do?
Kinetics (Spool rolls on Cables)
α
ϖ
r
a
r
a
r
a
r
r
a
a
Gy
A
G
G
A
G
A
A
G
A
G
A
G

=
×
=
=

×
+
=
/
2
/
2
/
/
2
2
2
2
2
2
2
2
2
2
A spool has a mass of 8 kg and a radius of gyration (k
G
) of 0.35 m.
Cords
of negligible mass are wrapped around its inner hub and outer rim.
There
is no slipping. Find the angular acceleration (
α
) of the spool.
ma
Gx
ma
Gy
I
α
G
Note that I assumed all
accelerations are in the
positive direction – I’ll let
the algebra do the work.
EOM
(1)
(2)
(3)
α=10.32 rad/s
2
T=19.77 N
a
Gy
= 5.16 m/s
2
3 Equations and 3 Unknowns, Do the algebra!
Problem Type:
Find:
Given:
F=100 N, k
G
= 0.35 m, μ
k
= 0.2, m=8 kg, Figure
α
First Step? FBD, MAD!!
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 Spring '05
 staff

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