53. We use τ = F r = Iα, where α satisfies θ =
12
αt
2
(Eq. 11-13). Here θ = 90
◦
=
π
rad and t = 30 s. The
force needed is consequently
F =
Iα
r
I
2θ/t
(8.7
× 10
4
)
2(π/2)/30
2.4
= 1.3
N .