p11_004.pdf
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Pobierz
Chapter 11 - 11.4
4. If we make the units explicit, the function is
θ
=(4
.
0rad
/
s)
t
−
3
.
0rad
/
s
2
t
2
+
1
.
0rad
/
s
3
t
3
but generally we will proceed as shown in the problem – letting these units be understood. Also, in
our manipulations we will generally not display the coe$cients with their proper number of significant
figures.
(a) Eq. 11-6 leads to
dt
4
t
−
3
t
2
+
t
3
=4
−
6
t
+3
t
2
.
Evaluatingthis at
t
= 2 s yields
ω
2
=4
.
0 rad/s.
(b) Evaluatingthe expression in part (a) at
t
=4sgives
ω
4
= 28 rad/s.
(c) Consequently, Eq. 11-7 gives
α
avg
=
ω
4
−
ω
2
=12rad
/
s
2
.
4
−
2
(d) And Eq. 11-8 gives
dt
=
d
dt
4
6
t
+3
t
2
=
−
−
6+6
t.
Evaluatingthis at
t
= 2 s produces
α
2
=6
.
0 rad/s
2
.
(e) Evaluatingthe expression in part (d) at
t
= 4 s yields
α
4
= 18 rad/s
2
. Wenotethatouranswer
for
α
avg
does turn out to be the arithmetic average of
α
2
and
α
4
but point out that this will not
always be the case.
ω
=
d
α
=
dω
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