p11_004.pdf

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.

α avg = ω 4 −

ω 2

=12rad / s 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