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(f) With radians and seconds understood, the graph of
θ
versus
t
is shown below (with the
points found in the previous parts indicated as small circles).
15. The problem has (implicitly) specified the positive sense of rotation. The angular
acceleration of magnitude 0.25 rad/s
2
in the negative direction is assumed to be constant
over a large time interval, including negative values (for
t
).
(a) We specify
max
with the condition
ω
= 0 (this is when the wheel reverses from
positive rotation to rotation in the negative direction). We obtain
max
using Eq. 1014:
2
2
o
max
2
(4.7 rad/s)
44 rad.
22
(
0
.
2
5
r
a
d
/
s
)
α
=−
=
−
(b) We find values for
t
1
when the angular displacement (relative to its orientation at
t
= 0)
is
1
= 22 rad (or 22.09 rad if we wish to keep track of accurate values in all intermediate
steps and only round off on the final answers). Using Eq. 1013 and the quadratic formula,
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 Spring '08
 Any
 Physics, Acceleration

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