Exercicios Resolvidos do Halliday sobre Rotação- Cap11- Exercicio 15

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15. The problem has (implicitly) specified the positive sense of rotation. The angular acceleration of magni-
tude 0.25 rad/s2 in the negative direction is assumed to be constant over a large time interval, including
negative values (for t).
(a) We specify θmax with the condition ω = 0 (this is when the wheel reverses from positive rotation
to rotation in the negative direction). We obtain θmax using Eq. 11-14:
θmax = − ω
2
o
2α
= − 4.7
2
2(−0.25) = 44 rad .
(b) We find values for t1 when the angular displacement (relative to its orientation at t = 0) is θ1 =
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. 11-13 and the quadratic formula, we have
θ1 = ωot1 +
1
2
αt21 =⇒ t1 =
−ωo ±
√
ω2o + 2θ1α
α
which yields the two roots 5.5 s and 32 s.
(c) We find values for t2 when the angular displacement (relative to its orientation at t = 0) is θ2 =
−10.5 rad. Using Eq. 11-13 and the quadratic formula, we have
θ2 = ωot2 +
1
2
αt22 =⇒ t2 =
−ωo ±
√
ω2o + 2θ2α
α
which yields the two roots −2.1 s and 40 s.
(d) 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).
θ
–20
20
40
10 20 30 40
t
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