Chapter 8.2, Problem 23PP

a

To determine

To Calculate: The moment of inertia of a thin hoop.

Answer to Problem 23PP

  $4.\text{0 kg}\cdot {\text{m}}^{\text{2}}$

Explanation of Solution

Given:

Radius, $r=2.0\text{m}$

Mass, $m=1.0\text{kg}$

Formula Used:

Moment of inertia of a hoop can be obtained by:

  $I=m{r}^2$

Calculations:

Substitute the values and solve:

  $\begin{array}{c}I=m{r}^2\\ =\left(1.0\right){\left(2.0\right)}^2\\ =4.\text{0 kg}\cdot {\text{m}}^{\text{2}}\end{array}$

Conclusion:

Thus, the moment of inertia of a hoop is $4.\text{0 kg}\cdot {\text{m}}^{\text{2}}$ .

b

To determine

To Calculate: The moment of inertia of a solid, uniform cylinder.

Answer to Problem 23PP

  $2.\text{0 kg}\cdot {\text{m}}^{\text{2}}$

Explanation of Solution

Given:

Radius, $r=2.0\text{m}$

Mass, $m=1.0\text{kg}$

Formula Used:

Moment of inertia of a solid, uniform cylinder can be obtained by:

  $I=\frac{1}{2}m{r}^2$

Calculations:

Substitute the values and solve:

  $\begin{array}{c}I=\frac{1}{2}m{r}^2\\ =\frac{1}{2}\left(1.0\right){\left(2.0\right)}^2\\ =2.\text{0 kg}\cdot {\text{m}}^{\text{2}}\end{array}$

Conclusion:

Thus, the moment of inertia of a hoop is $2.\text{0 kg}\cdot {\text{m}}^{\text{2}}$ .

c

To determine

To Calculate: The moment of inertia of a solid, uniform sphere.

Answer to Problem 23PP

  $1.6\text{ kg}\cdot {\text{m}}^{\text{2}}$

Explanation of Solution

Given:

Radius, $r=2.0\text{m}$

Mass, $m=1.0\text{kg}$

Formula Used:

Moment of inertia of a solid, uniform sphere can be obtained by:

  $I=\frac{2}{5}m{r}^2$

Calculations:

Substitute the values and solve:

  $\begin{array}{c}I=\frac{2}{5}m{r}^2\\ =\frac{2}{5}\left(1.0\right){\left(2.0\right)}^2\\ =1.6\text{ kg}\cdot {\text{m}}^{\text{2}}\end{array}$

Conclusion:

Thus, the moment of inertia of a hoop is $1.6\text{ kg}\cdot {\text{m}}^{\text{2}}$ .