Chapter 10

$\omega =0\text{.}\text{737 rev/s}$

(a) $-0\text{.}{\text{26 rad/s}}^2$

(b) $\text{27}\text{rev}$

(a) $80{\text{rad/s}}^2$

(b) 1.0 rev

(a) 45.7 s

(b) 116 rev

a) $6{\text{00 rad/s}}^2$

b) 450 rad/s^s

c) 21.0 m/s^s

(a) 0.338 s

(b) 0.0403 rev

(c) 0.313 s

$\text{0.50 kg}\cdot {\text{m}}^2$

(a) $\mathrm{50.4\; N}\cdot \text{m}$

(b) $\text{17.1}{\text{rad/s}}^2$

(c) $17.0{\text{rad/s}}^2$

$3\text{.}\text{96}\times {\text{10}}^{\text{18}}\text{s}$

or $1.26\times {\text{10}}^{\text{11}}\text{y}$

$\begin{array}{c}{I}_{\text{end}}=I_{\text{center}}+m{\left(\frac{l}{2}\right)}^2\\ \text{Thus,}{I}_{\text{center}}=I_{\text{end}}-\frac{1}{4}{\text{ml}}^2=\frac{1}{3}{\text{ml}}^2-\frac{1}{4}{\text{ml}}^2=\frac{1}{\text{12}}{\text{ml}}^2\end{array}$

(a) 2.0 ms

(b) The time interval is too short.

(c) The moment of inertia is much too small, by one to two orders of magnitude. A torque of $\text{500 N}\cdot \text{m}$ is reasonable.

(a) 17,500 rpm

(b) This angular velocity is very high for a disk of this size and mass. The radial acceleration at the edge of the disk is > 50,000 gs.

(c) Flywheel mass and radius should both be much greater, allowing for a lower spin rate (angular velocity).

(a) 185 J

(b) 0.0785 rev

(c) $W=9\text{.}\text{81 N}$

(a) $2.57\times {\text{10}}^{\text{29}}\text{J}$

(b) ${\text{KE}}_{\text{rot}}=2\text{.}\text{65}\times {\text{10}}^{\text{33}}\text{J}$

(a) $\text{128 rad/s}$

(b) $\text{19.9 m}$

(a) $\text{10.}{\text{4 rad/s}}^2$

(b) $\text{net}W=6.\text{11 J}$

(a) 1.49 kJ

(b) $2.52\times {\text{10}}^4\text{N}$

(a) $2\text{.}\text{66}\times {\text{10}}^{\text{40}}\text{kg}\cdot {\text{m}}^2\text{/s}$

(b) $7\text{.}\text{07}\times {\text{10}}^{\text{33}}\text{kg}\cdot {\text{m}}^2\text{/s}$

The angular momentum of the Earth in its orbit around the Sun is $3\text{.}\text{77}\times {\text{10}}^6$ times larger than the angular momentum of the Earth around its axis.

$\text{22}\text{.}\text{5 kg}\cdot {\text{m}}^2\text{/s}$

25.3 rpm

(a) $\mathrm{0.156\; rad/s}$

(b) $1\text{.}\text{17}\times {\text{10}}^{-2}\text{J}$

(c) $0\text{.}\text{188 kg}\cdot \text{m/s}$

(a) 3.13 rad/s

(b) Initial KE = 438 J, final KE = 438 J

(a) 1.70 rad/s

(b) Initial KE = 22.5 J, final KE = 2.04 J

(c) $1\text{.}\text{50 kg}\cdot \text{m/s}$

(a) $5\text{.}\text{64}\times {\text{10}}^{\text{33}}\text{kg}\cdot {\text{m}}^2\text{/s}$

(b) $1\text{.}\text{39}\times {\text{10}}^{\text{22}}\text{N}\cdot \text{m}$

(c) $2\text{.}\text{17}\times {\text{10}}^{\text{15}}\text{N}$